{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "##################################################\n",
    "# Execute this cell and start the tutorial below #\n",
    "##################################################\n",
    "\n",
    "# for plotting\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('seaborn-whitegrid')\n",
    "\n",
    "# for the math\n",
    "import numpy as np\n",
    "from sklearn.decomposition import PCA\n",
    "\n",
    "def create_dataset(n, p, q, σ=0.0, rank_B=None):\n",
    "    \n",
    "    # make sure we get the same dataset every time\n",
    "    np.random.seed(31415)\n",
    "    \n",
    "    # if no rank was given, create a full-rank B\n",
    "    if rank_B is None:\n",
    "        rank_B = min(p, q)\n",
    "    \n",
    "    # create a random B with given rank: B = UV, with\n",
    "    #   U pxr random matrix (full rank)\n",
    "    #   V rxq random matrix (full rank)\n",
    "    U = np.random.normal(size=(p, rank_B))\n",
    "    V = np.random.normal(size=(rank_B, q))\n",
    "    B = U@V\n",
    "    assert(np.linalg.matrix_rank(B) == rank_B)\n",
    "    \n",
    "    # create random X\n",
    "    X = np.random.normal(size=(n, p))\n",
    "    \n",
    "    # compute Y = XB\n",
    "    Y = X@B\n",
    "    \n",
    "    # add measurement noise\n",
    "    if σ > 0:\n",
    "        X += np.random.normal(scale=σ, size=X.shape)\n",
    "        Y += np.random.normal(scale=σ, size=Y.shape)\n",
    "\n",
    "    return X, Y, B\n",
    "\n",
    "def scatter_plots(datasets, titles, **kwargs):\n",
    "    n = len(datasets)\n",
    "    fig, axises = plt.subplots(nrows=1, ncols=n, figsize=(20, 20/n))\n",
    "    for axis, data, title in zip(axises, datasets, titles):\n",
    "        colors = np.arange(data.shape[0])\n",
    "        axis.scatter(data[:,0], data[:,1], c=colors, alpha=0.6, cmap='viridis', **kwargs)\n",
    "        axis.set_title(title)\n",
    "\n",
    "def plot_validation_losses(n, p, q, σ, rank_B=None):\n",
    "    \n",
    "    # create dataset\n",
    "    X, Y, B = create_dataset(n=n, p=p, q=q, σ=σ, rank_B=rank_B)\n",
    "    \n",
    "    rrr_ranks = list(range(9, min(100, p, q) + 1))\n",
    "    error_ols_t, error_ols_v = evaluate(X, Y, B, solve_ols)\n",
    "    errors_rrr = np.array([evaluate(X, Y, B, solve_rrr, rank=rank) for rank in rrr_ranks])\n",
    "    errors_rrr_t = errors_rrr[:, 0]\n",
    "    errors_rrr_v = errors_rrr[:, 1]\n",
    "\n",
    "    fig, axises = plt.subplots(nrows=1, ncols=2, figsize=(20, 20/2))\n",
    "    axises[0].plot(rrr_ranks, [error_ols_t]*len(rrr_ranks), label=\"OLS train\", color='blue')\n",
    "    axises[1].plot(rrr_ranks, [error_ols_v]*len(rrr_ranks), label=\"OLS validate\", color='blue')\n",
    "    axises[0].plot(rrr_ranks, errors_rrr_t, label=\"RRR train\", color='orange')\n",
    "    axises[1].plot(rrr_ranks, errors_rrr_v, label=\"RRR validate\", color='orange')\n",
    "    axises[0].set_xlabel(\"rank of RRR\")\n",
    "    axises[1].set_xlabel(\"rank of RRR\")\n",
    "    axises[0].set_ylabel(\"training loss\")\n",
    "    axises[1].set_ylabel(\"validation loss\")\n",
    "    axises[0].legend()\n",
    "    axises[1].legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "# A Gentle Introduction to Reduced Rank Regression"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Preliminaries\n",
    "\n",
    "<center><img width=\"25%\" src=\"img/intro_z_x.png\"></img></center>\n",
    "\n",
    "$X \\in \\mathbb{R}^{n\\times p}\\;\\ldots$ noisy observed data ($n$ samples, $p$ features)\n",
    "\n",
    "$Z \\in \\mathbb{R}^{n\\times r}\\;\\ldots$ unknown latent structure ($r$ latent dimensions)\n",
    "\n",
    "We assume that $r < p$. What can we learn about $Z$ if we only observe $X$?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Find latent structure through dimensionality reduction:\n",
    "\n",
    "<div class=\"alert alert-block alert-success\">\n",
    "    <b>Linear analysis:</b>\n",
    "     PCA, ICA, ...\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "<div class=\"alert alert-block alert-warning\">\n",
    "    <b>Non-linear methods:</b>\n",
    "    t-SNE, autoencoders, ...\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Regression Problems\n",
    "\n",
    "<center><img width=\"25%\" src=\"img/intro_z_x_y.png\"></img></center>\n",
    "\n",
    "$X \\in \\mathbb{R}^{n\\times p}\\;\\ldots$ noisy observed predictors ($n$ samples, $p$ features)\n",
    "\n",
    "$Y \\in \\mathbb{R}^{n\\times q}\\;\\ldots$ noisy observed responses ($q$ features)\n",
    "\n",
    "$Z \\in \\mathbb{R}^{n\\times r}\\;\\ldots$ unknown latent structure ($r$ latent dimensions)\n",
    "\n",
    "What can we learn about the relationship between $X$ and $Y$?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "<div class=\"alert alert-block alert-success\">\n",
    "    <b>Linear Multivariate Regression:</b>\n",
    "    $Y=XB + \\epsilon$<br/>\n",
    "    with $B \\in \\mathbb{R}^{p\\times q}$ (coefficent matrix)<br/>\n",
    "    and $\\epsilon \\in \\mathbb{R}^{n\\times q},\\;\\epsilon_i \\sim \\mathcal{N}(0, \\sigma_\\epsilon)$ (error matrix)\n",
    "</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Ordinary Least Squares (OLS)\n",
    "\n",
    "Find $B$ by minimizing difference between $Y$ and $XB$:\n",
    "<center>$\\hat{B}_{\\text{OLS}} = \\arg \\min_{B} || Y - XB ||^2$</center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "<center>$\n",
    "\\begin{align*}\n",
    "\\frac{\\partial}{\\partial B} || Y - XB ||^2 &= 0 \\\\\n",
    "2 (Y - XB)^T X &= 0 \\\\\n",
    "X^T (Y - XB) &= 0 \\\\\n",
    "X^T Y - X^TXB &= 0 \\\\\n",
    "X^TXB &= X^T Y\\;\\;\\;\\;\\;| (X^T X)^{-1} \\cdot \\\\\n",
    "B &= (X^TX)^{-1} X^T Y \\\\\n",
    "\\end{align*}\n",
    "$</center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Implementation in numpy:\n",
    "<br/>\n",
    "<br/>\n",
    "<center>$B = (X^TX)^{-1} X^T Y$</center>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 211,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "# Find B* = argmin_B |Y - XB|²\n",
    "def solve_ols(X, Y):\n",
    "    return np.linalg.pinv(X.T@X)@X.T@Y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "<div class=\"alert alert-block alert-warning\">\n",
    "    <b>Note:</b>\n",
    "    Don't use numpy.linalg.inv()!\n",
    "    See <a href=\"https://stackoverflow.com/questions/49357417/why-is-numpy-linalg-pinv-preferred-over-numpy-linalg-inv-for-creating-invers#49364727\">this stackoverflow</a> answer for some details.\n",
    "</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 178,
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "|B - B_ols|²: 3.0847422370805075e-15\n"
     ]
    },
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 1440x480 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# create a random dataset with known B (noise free):\n",
    "X, Y, B = create_dataset(n=100, p=2, q=2)\n",
    "\n",
    "# find B_ols\n",
    "B_ols = solve_ols(X, Y)\n",
    "\n",
    "# plot X, Y, and XB\n",
    "scatter_plots([X, Y, X@B_ols], [\"X\", \"Y\", \"X*B_ols\"])\n",
    "\n",
    "print(f\"|B - B_ols|²: {np.linalg.norm(B - B_ols)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Are we done already?\n",
    "\n",
    "There are potential problems with OLS:\n",
    "1. Blind to multivariate aspect of problem: $y_i$ might be correlated, effective dimensionality smaller than $q$ \n",
    "2. Unsuitable if $p,q > n$: regularization needed"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "<div class=\"alert alert-block alert-info\"><b>Try yourself:</b> Change $p$ and $q$ in the following cell to values larger than $n$, and observe how the prediction performance suffers:</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 243,
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "|B - B_ols|²: 9.155133597044475e-16\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x480 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# create a random dataset with known B:\n",
    "X, Y, B = create_dataset(n=100, p=2, q=2) # increase p and q\n",
    "\n",
    "# find B_ols using half of the dataset\n",
    "B_ols = solve_ols(X[:50], Y[:50])\n",
    "\n",
    "# plot X, Y, and the prediction XB on the second half of the dataset\n",
    "scatter_plots([X[50:], Y[50:], X[50:]@B_ols], [\"X\", \"Y\", \"X*B_ols\"])\n",
    "\n",
    "print(f\"|B - B_ols|²: {np.linalg.norm(B - B_ols)}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "<div class=\"alert alert-block alert-success\"><b>Bottom line:</b> If $p, q > n$, we need to regularize $B$</div>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## X,Y Dimensionality Reduction Techniques\n",
    "##  \n",
    "\n",
    "<center>Linear Factor Regression</center>\n",
    "\n",
    "1. PCA: Principle Component Regression\n",
    "2. Project $X$ and $Y$ to common subspace: Partial Least Squares\n",
    "3. Canonical Correlation Analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Explicit Regularization Term on $B$\n",
    "##  \n",
    "\n",
    "<center>$\\hat{B} = \\arg \\min_{B} || Y - XB ||^2 + R(B)$</center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "1. lasso regression: $ R(B) = \\lambda_1\\sum_{j=1}^p ||B_j||_1$ (least absolute shrinkage and selection operator)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "2. ridge regression: $ R(B) = \\lambda_2\\sum_{j=1}^p ||B_j||_2$ (L2 regularizer)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "3. mixture of the two: [Peng (2009)](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3905690/), [Obozinski (2011)](https://projecteuclid.org/download/pdfview_1/euclid.aos/1291388368)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Another way: Constrain the Rank of $B$\n",
    "##   \n",
    "\n",
    "<center>Reduced Rank Regression:</center>\n",
    "<br/> \n",
    "<center>$\\hat{B}_r = \\arg \\min_{B: \\text{rank}(B)\\leq r} ||Y - XB||^2$</center>\n",
    "\n",
    "Termed and studied by [Izenman (1975)](https://linkinghub.elsevier.com/retrieve/pii/0047259X75900421), earlier introduced by [Anderson (1951)](https://projecteuclid.org/euclid.aoms/1177729580)\n",
    "\n",
    "This constraint turnes the objective into a non-convex optimization problem (however, a closed form solution exists).\n",
    "\n",
    "($\\text{rank}(B)$: dimensionality of the subspace spanned by the rows or columns of $B$)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## How to Solve for $\\hat{B}_r$\n",
    "\n",
    "<br/>\n",
    "<br/>\n",
    "<center>$\\hat{B}_r = \\arg \\min_{B: \\text{rank}(B)\\leq r} ||Y - XB||^2$</center>\n",
    "\n",
    "Steps:\n",
    "1. Decompose the loss using the OLS solution\n",
    "2. Learn about the Eckart-Young-Mirsky theorem\n",
    "3. Invent a potential minimizer $\\hat{B}_r$ based on intuition\n",
    "4. Use the Eckart-Young-Mirsky theorem to prove that it minimizes our objective\n",
    "\n",
    "(this proof losely follows the derivation in [Mukherjee (2011)](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3444519/))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Step 1: Decompose the loss using the OLS solution\n",
    "\n",
    "Let $\\hat{B}^\\text{ols} = \\arg\\min_B ||Y-XB||^2$ and $\\hat{Y}^\\text{ols} = X\\hat{B}^\\text{ols}$. Since the OLS solution is <a href=\"https://people.math.osu.edu/husen.1/teaching/571/least_squares.pdf\">an orthogonal projection</a>, we can rewrite the loss as:\n",
    "<br/>\n",
    "<br/>\n",
    "<center>\n",
    "    $||Y-XB||^2 = ||Y - \\hat{Y}^\\text{ols}||^2 + ||\\hat{Y}^\\text{ols} - XB||^2$\n",
    "</center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "<center>\n",
    "<img src=\"img/orthogonal.png\"></img>\n",
    "</center>\n",
    "<center>\n",
    "(image from <a href=\"https://textbooks.math.gatech.edu/ila/projections.html\">this tutorial</a> on orthogonal projections)\n",
    "</center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "source": [
    "Since the first term does not depend on $B$, we can find\n",
    "<center>$\n",
    "    \\begin{align}\n",
    "        \\hat{B}_r = \\arg\\min_{B: \\text{rank}(B)\\leq r} ||\\hat{Y}^\\text{ols} - XB||^2\n",
    "                  = \\arg\\min_{B: \\text{rank}(B)\\leq r} ||X\\hat{B}^\\text{ols} - XB||^2\\\\\n",
    "    \\end{align}\n",
    "$</center>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Step 2: Learn about the Eckart-Young-Mirsky theorem\n",
    "\n",
    "Let the singular value decomposition of a matrix $A = U\\Sigma V^T$, with $\\Sigma=\\text{diag}(\\pmb{\\sigma})$ and $U, V$ orthogonal matrices. We will refer to the ith column of $U$ and $V$ as $\\pmb{u}_i$ and $\\pmb{v}_i$.\n",
    "\n",
    "<center>$\n",
    "    \\begin{align}\n",
    "        \\arg\\min_{A_r: \\text{rank}(A_r)\\leq r} ||A - A_r||^2 = \\sum_{i=1}^r \\pmb{\\sigma}_i \\pmb{u}_i \\pmb{v}_i^T\n",
    "    \\end{align}\n",
    "$</center>\n",
    "\n",
    "(for a proof see, e.g., the [Wikipedia](https://en.wikipedia.org/wiki/Low-rank_approximation#Proof_of_Eckart%E2%80%93Young%E2%80%93Mirsky_theorem_(for_Frobenius_norm)) page)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Step 3: Invent a potential minimizer\n",
    "\n",
    "Let the singular value decomposition of $\\hat{Y}^\\text{ols} = U\\Sigma V$ (with $\\pmb{\\sigma}_i$, $\\pmb{u}_i$, and $\\pmb{v}_i$ as defined before).\n",
    "\n",
    "We invent a projection matrix $P_r := \\sum_{i=1}^r \\pmb{v}_i\\pmb{v}_i^T$, i.e., the outer product of the first $r$ right hand singular vectors of $\\hat{Y}^\\text{ols}$.\n",
    "\n",
    "We use this projection to construct a rank-reduced $\\hat{B}_r := \\hat{B}^\\text{ols} P_r$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "### Step 4: Prove that $\\hat{B}_r$ minimizes the loss\n",
    "\n",
    "Recall:\n",
    "1. Our loss is $||\\hat{Y}^\\text{ols} - XB||^2$\n",
    "2. We know that $||\\hat{Y}^\\text{ols} - \\hat{Y}^\\text{ols}_r||^2$ is minimized with $\\hat{Y}^\\text{ols}_r = \\sum_{i=1}^r \\pmb{\\sigma}_i\\pmb{u}_i\\pmb{v}_i^T$ of given rank $r$\n",
    "3. We constructed $\\hat{B}_r := \\hat{B}^\\text{ols} P_r$\n",
    "\n",
    "We need to show that $X\\hat{B}_r = \\hat{Y}^\\text{ols}_r$:\n",
    "\n",
    "<center>$\n",
    "    \\begin{align}\n",
    "        X\\hat{B}_r &= X\\hat{B}^\\text{ols}P_r\n",
    "                   = \\hat{Y}^\\text{ols}P_r \\\\\n",
    "                   &= \\left( \\sum_{i=1}^q \\pmb{\\sigma}_i\\pmb{u}_i\\pmb{v}_i^T \\right)\n",
    "                      \\left( \\sum_{i=1}^r \\pmb{v}_i\\pmb{v}_i^T \\right)\n",
    "                   = \\sum_{i=1}^r \\pmb{\\sigma}_i\\pmb{u}_i\\pmb{v}_i^T \\;\\;\\;\\text{(see sub-slide)} \\\\\n",
    "                   &= \\hat{Y}^\\text{ols}_r\n",
    "    \\end{align}\n",
    "$</center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "Why does the following equality hold?\n",
    "<center>$\n",
    "\\left( \\sum_{i=1}^q \\pmb{\\sigma}_i\\pmb{u}_i\\pmb{v}_i^T \\right) \\left( \\sum_{i=1}^r \\pmb{v}_i\\pmb{v}_i^T \\right)\n",
    "                   = \\sum_{i=1}^r \\pmb{\\sigma}_i\\pmb{u}_i\\pmb{v}_i^T\n",
    "$</center>\n",
    "\n",
    "Column vectors of $V$ are orthogonal:\n",
    "<center>$\n",
    "\\begin{align}\n",
    "    \\left( \\sum_{i=1}^q \\pmb{\\sigma}_i\\pmb{u}_i\\pmb{v}_i^T \\right) \\left( \\sum_{i=1}^r \\pmb{v}_i\\pmb{v}_i^T \\right)\n",
    "        &= \\sum_{i=1}^q \\pmb{\\sigma}_i\\left( \\sum_{j=1}^r (\\pmb{u}_i\\pmb{v}_i^T)(\\pmb{v}_j\\pmb{v}_j^T) \\right) \\\\\n",
    "        &= \\sum_{i=1}^q \\pmb{\\sigma}_i\\left( \\sum_{j=1}^r (\\pmb{v}_j^T\\pmb{v}_i)(\\pmb{u}_i\\pmb{v}_j^T) \\right) \\\\\n",
    "        &= \\sum_{i=1}^r \\pmb{\\sigma}_i\\pmb{u}_i\\pmb{v}_i^T \\\\\n",
    "\\end{align}\n",
    "$</center>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Implementation in numpy:\n",
    "\n",
    "<center>$\\hat{B}_r = \\arg\\min_{B: \\text{rank}(B)\\leq r} ||\\hat{Y}^\\text{ols} - XB||^2 = \\hat{B}^\\text{ols} \\left( \\sum_{i=1}^r \\pmb{v}_i\\pmb{v}_i^T \\right)$</center>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 148,
   "metadata": {
    "slideshow": {
     "slide_type": "fragment"
    }
   },
   "outputs": [],
   "source": [
    "def solve_rrr(X, Y, rank):\n",
    "    \n",
    "    # get OLS solution\n",
    "    B_ols = solve_ols(X, Y)\n",
    "    \n",
    "    # get OLS estimate\n",
    "    Y_ols = X@B_ols\n",
    "    \n",
    "    # get singular values and vectors of Y_ols\n",
    "    U, Σ, V = np.linalg.svd(Y_ols)\n",
    "    \n",
    "    # construct P_r\n",
    "    P_r = np.sum([np.outer(V[i], V[i]) for i in range(rank)], axis=0)\n",
    "    \n",
    "    return B_ols@P_r"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "<div class=\"alert alert-block alert-info\"><b>Try yourself:</b> Change $\\text{rank}$ in the following cell to 1 and see how the prediction changes:</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 244,
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "|B - B_rrr|²: 8.881784197001252e-16\n"
     ]
    },
    {
     "data": {
      "image/png": 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0VFNEJN+onRARGTuGXOR527p163jooYf46U9/etS+efPmnerL+6K+vj5ns48UXZNj03U5mq7J0d57TTZu3OhjmuERCAQG/u953lHDMN+9/3jPgaHfDMilwlmuZM2VnJA7WXMlJ+RO1lzJCbmVdSSonTg5uZITcidrruSE3MmaKzkhd7KOZM5TKvI899xz/Mu//As//vGPicViw5VJRETGuKKiIhKJBAUFBbS2tg7qog9QWVlJW1vbwOP29nYqKiqOep2hFgRzqZiYK1lzJSfkTtZcyQm5kzVXcsKpZc2HmwFqJ05OruSE3MmaKzkhd7LmSk7InaynmvNE7cSQ5+Tp6enhzjvv5Ec/+hGlpaVDfRkREclBK1as4KmnngLgySefZOXKlYP2n3/++QP733zzTSZNmjTQbV9ERPKf2gkREX8MuSfP448/TldXF1/+8pcHtt11111MmDBhWIKJiMjYsGXLFu666y4aGhqwbZu1a9fyve99j7/7u7/jpz/9KdOmTeOKK64A4Mtf/jLf/e53WbBgAXPnzuWTn/wklmXxne98x+ezEBGRkaJ2QkRk7Bhykef666/n+uuvH84sIiIyBi1YsID777//qO3H2vb9739/4P9f+cpXRjSXiIiMDWonRETGjiEP1xIRERERERERkbFDRR4RERERERERkTygIo+IiIiIiIiISB5QkUdEREREREREJA+oyCMiIiIiIiIikgeGvLqW5AfP89jf00lrPE5NJEpdJOZ3JBEREREREREZAhV5xrFENsMPNr3IW23NmBi4eCytmciti5YSMC2/44mIiIiIiIjIB6Aizzj28PY32dLazISiCIZh4HkeLx3az5RYCVfOmOt3PBERERERERH5ADQnzzjleh5/OrCbqsJCDMMAwDAMygsKeWrfLp/TiYiIiIiIiMgHpSLPOOV6HlnXxTIG/whYhknKcXxKJSIiIiIiIiJDpSLPOGWbJkuqamlNxAdtb0vGOad2ok+pRERERERERGSoVOQZxz41bxHRYJDDvT00x3s53NdDdWGET8ya73c0EREREREREfmANPHyOFZVGOE7Kz7CK40NNPR2MzVWwhnVdYRt/ViIiIiIiIiI5Bp9mh/nigJBVk6a5ncMERERERERETlFKvKI5IBEIs3ObY1kMw5TZ1RSWhbxO5KIiIiIiIiMMSryiIxxu3c2cf+PnyWdyuB5/UvdX/axxaz48Dy/o4mIiIiIiMgYoiKPjFuHD3aw9c0GTNNg7oI6qmtL/I50lHQqy4M/fY5AwKK4uBCAbMbhD49tZsasaiZMLPM5oYiIiIiIiIwVKvLIuPTHtW+w7vHXAQ/DM3jisVf56NVn8aGVc/yONsi+vS2kkhkqKmMD2+yAhYHBm68fVJFHREREREREBqjII+NOc2MX6373OmUVRdi2BUAm4/D4I68w//SJlJQV+ZzwHZ7rHXuHAa7rjm4YERERERERGdNMvwOIjLbd2xvxPG+gwAMQCFh4Luze0eRjsqNNnlZJIGCRTKQHtjmOi+d6zFtQ52MyERERERERGWtU5JFxx7JNjGPtMDxse2z9SoTDAa5b/SHi8RTNTV00N3bR3tbD+RfNZ9KUCr/jiYiIiIiIyBii4Voy7syeX4dlW6SSGULhANC/RHkgYDNjTq3P6Y4277SJ/N03rmLbW4dIpx2mz6qidkKp37FERERERERkjFGRR8ad4pJCrrvpXB5+4AV6uhJ4QDBo8+nPraAoEvI73jHFigtZunym3zFERERERERkDFORR8alBYsnM31WNXt3NWMYBtNmVhEuCPodS0TklHieh5t6Djf5OLidGIGFWIWfwLAm+B1NRETGAM/L4ibX4SbXgRfHCJ6FVfBxDKvc72giMkxU5JFxq7AoxPyFk/yOISIybNzkYzjxh8EsBTOGl9mM170FO/bfMaxKv+OJiIjPnL77cVPPgFkGZgQv/Txe5k3s4v+OYUb8jiciw2BszTIrIiIiQ+J5CZzEY2DVYJgRDCOAYVXheUmc5NN+xxMREZ95Tgtu6lmwJmCYhUfaiVo8tx03vd7veCIyTNSTR0REJB84bRh4YAQGbzcieM4ufzKJiMiY4blNYFgYxnvu8xtBvOwef0KJyLBTTx4REZF8YJbg0T/fwiBeH4Y12ZdIIiIydhhmBeDged579qQxLE1hIJIv1JNHZBgcSjTxeudWkm6KOdHpzI5OwzIsv2OJyDhimBHM0MW4ycfxrCogCF4HYGGFL/Q7noiI+MywajADZ+GmX8azqgEL3DYMI4IZWu53PBEZJiryiJyije1b+H3jM5iGiWVYvN65jdnRaVw76XIVekRkVFmF12CYEdzEH/C8VozALKzCT2l1LRERAcCK/CXEK/BST+ORxgwsxCq8HsOM+R1NRIaJijwipyDlpXmi6QWKAzECZv+vk2d77OjZw67e/cyOTvM5oYiMJ4ZhYxVciRn+KOBgGGrmRUTkHYYRwi66Hq/wWsBVOyGSh/RbPQI8L4ub3QVeCtOeiWEW+h1JRkib04VruQMFHgDDMAiYAXb27FWRR0SGzPM8Duxr49DBdgqLQsyeN4FwOPD+B9L/d0hNvIhIfnNdjz27mmhu7Ka4pJBZc2sJBE6uF3n/5MuanlUkH+kd4DBzs/tI9Xwf1+3EADxsgkWfIxD+kN/RZAQEjjMcy/EcCuyCUU4jMnp++ctf8uijjw483rJlC5s3bx54fN555zFt2jtFzvvuuw/L0vDFk+VkXR7+zxd5bdM+8MAwoagoxC2fv5DaulK/44mIvC+1EyMrncpy/0/+xK7tTeB5GIZBaXmEv1hzEaVlRX7HExEfqcgzjDwvQ6rnn/C8FKZVc2RjknTfv2IFpmJqToS8U26WUhYsoSvdTSwQxTAMUk4agAXFs31OJzJyrr32Wq699loAXnnlFR577LGBfZ7nUVVVxf333+9XvJz3xmv7ePWVvVTVFB/plQNdnXEeeuAFvvjVKwa2iYiMVWonRtYLz21j57ZGqqrfaSfaW3t47Nev8Nm/XOlzOhHxk/roDSM3u6O/B49ZMrDNMMKAQTa13r9gMmJMw+D6yR+lJFhMW7qT9nQHKTfNJ+s+QmWozO94IqPiBz/4AWvWrBl4HI/HcRzHx0S5b/OGvRQUBgcVc2LFBTQ3ddHe2utjMhGRD07txPDbtH43seLCQe1ESVmEbW8dIpXM+JhMRPymnjzDycsAx7m76iVGNYqMnrJgCbdOv4GmVCtpN0NNuJKgeXLzZojkutdff53q6mqqq6sHtsXjcdra2lizZg3t7e1cccUVfPazn/UxZQ46bkcd9eARkdyidmKEHKc5UCshIiryDCPTng6YeF4awwgC4Hku4GAFF/uaLZd4Xgq8PjBiOTPjv2EY1IQr/Y4hMuoeeughrrjiikHbCgoK+OIXv8hVV12F67qsXr2axYsXs3DhwqOOr6+vH9LXTSaTQz52tA0la0WVyaYNHThucuAubW9PilhxmKaWAzS3Dv/b+Hy/pn7IlZyQO1lzJSfkVtaRpHbixIaas2ZimJee3UNpecFAO9HZkWDq9DJ279k53DGB/L+mfsiVrLmSE3In60jmzI1P0DnCMKMEi24i3fcTPABM8LLY4fMx7bk+pxv7PC+Ll/gNpJ4CLwtmFK/gOszQMr+jichxbNiwgW9+85uDtkUiEa677rqBx8uWLWPHjh3HfPM+b968IX3d+vr6IR872oaSdfbsOaQSITZt2D0woWZFRRm3fP7DVNeWvP8LjFJOv+RK1lzJCbmTNVdywqll3bhx4zCn8Y/aiRMbas4ZM2aRTtjs2HoYzwMMmDK1hltuu4jikpFZ2Tffr6kfciVrruSE3Ml6qjlP1E6oyDPMAuGVWPb0I3PwJLCCSzDt+UeWKZQT8RK/heTvwKwGM9A/xK3vR3hmDCMw3+94IvIejY2NBINBQqHQoO07d+7knnvu4Xvf+x6O47Bp0yYuvfRSn1LmJssyufpT5/Ch82fTcKB/CfVZc2oJhtRsi0juUDsxcoJBm5tuvYB9e1pobuqmuLiQGbOrsW2tUCYy3und4ggw7UkE7Ul+x8gpnpeG1Lr+Ao9xZD4bowCMQrzkWhV5RMag5uZmqqqqBh7/6Ec/YunSpSxZsoSqqiquueYaTNPkwgsvPObdWTkxwzCYMLGMCRM1ibuI5Ca1EyPLMAymTq9i6vSq93+yiIwbKvLI2OAlcNw0nZkMnpemOBwmYFr9hR6n2e90InIMCxcu5Mc//vHA41tvvXXg/1/96lf9iCQf0KHubupbWghaFqF02u84IpJn1E7kNs/z2NvZya62NgqDQULZrN+RROQkqMgjY0J9a4LO5j6gm6QbwjQM5pZXUBXug9B5fscTEckrnufx2/p6Ht26Fc/zwDBIxeN8taqKxbW1fscTERGfuZ7Hv2/ezLN79+J5HgaQTSb5dl0dM8rUw1RkLNNEMeK7eCbDP29Yz/r2cykNZagKJym0HA537yLl2hhhjdEWERlOezs7+e3WrVQWFTEhFmNCNEqBbfOvGzaQyGT8jiciIj577fBhntmzh5pIhLpYjAmxGKZh8MP163E9z+94InICKvKI795qaSbtOLRk57K2+ZMcTk7CM0K83jGbDd23YFjVfkcUEckrmw4dwjQMbPOdtwFhyyLtOOxoa/MxmYiIjAUvHjhAgW1jHlmeHSASCNCRTHKgq8vHZCLyfjRcS3yXdV04suh8c2oCzakJABzq6aaqstjHZCIi+ckyDDjBnVjP8+jINBHPdhELVBALlI9iOhER8du7izvvZdDfTrSlG0g6cUqD1RTZes8uMlaoyCO+m1NegYFB2nEIWv3LPvYXfmBBpXrxiIgMtyUTJvDo1q1kHIfAkb+7iWyWcCjE9LIoTzc/yOHELgxMPFymFS2kMvMhXtvdiAecMaOOGTXlGCf4ECAiIrnrQ5Mn89KBAziui3Wk12dPOk1tLEZ5kcnvD99Le7qxv+ADzIsuJ9x7Om/sayQUtDlrxkQmVZb4eg4i45WKPDnG8zySyQy2bREIWH7HGRalBQWsPn0x//HGq3h4GBh4nsdVs+cyqVh3BUREhtuUkhKuXbCAh998s3/iZSDlOPztOefwVs8zHErspNiuxDAMPM/lxYbnObB9L07HNAD++MYuLjtjDh8/5zQ/T0NEREbI6dXVXDJzJk/t2tU/8bJhYBoGa845h/Xtj9GRbiJm9xf7HTfLk3sf51D9Lry+WjzP48nNO/jU+YtYcdp0v09FZNxRkSeHHDzQzqO/foWD+9uwLJOl58zg0isXEQoFBj0v4zjEMxkiweBA5X2s+/C06cypqGDT4cM4nsvC6hqmFud29b+hqZMn/7yVvQfbqCqPcvG5c5k9tcrvWCIiAFw+ezZL6+rY1tqKbZrYnZ3Mq6rgF/s3E7XLBnrpJNJZWtocSmoasdzTAXBcl7WbtnPO7MnUlEb9PA0RERkBhmHwmUWLuGDaNHa3t1MQCGB3dFAVtXmuc9dAgQegJ5Ghs9uhbEIzZvNMANJZh4f+/DqLp9cRLQj5eSoi446KPDmio6OPf/uXpzAMqKyK4jguLz6/nZ6eBJ+5eQXQv9ThH3Zu57EdW0k5DpFgkGvnLWDF5Kn+hj9JE6IxJkRjfscYFgcbO/nBfzyDB0SLQhxs7OSHDz7HLdcsY+GcOr/jiYgAUFFUREVREQD1vb2Ah+s5mO9al6E7nsTzTAzTGdhmmSae57HzcCtlMWhOvEJPZj9FgTpqCs4maOXH33IRkfGuLhajLtb/N72+uxvHy/LegbodvXHwDDCzA9uCtoXreuxpamf2xBBN8Q3EnSZigWlUFZ5JwCwcxbMQGV9U5MkRmzfsIZPOUlnd/0fWti2qamK8+cZBWlt6qKiM8tSeXfz8rTeoLCyitMAmkclw7+ZXKAoEOKNWhYXR9OSftwJQXtL/4SkYsLFti0efeoPTZ0/QPBYiMiZZhs2Egpk0JvYSDZQCYJomVjABfbMHPdcwwLS72djyY9JON5YZojm+iYO9T7O4/IsUBmr8OAURERlBRVYx0UA5SaePAisCgGUZGHYaeo7xecNq4pWWn+F6aUwjQHPiFQ72Pc3iii8RsjQtg8hIyI2xPEJTU7kqvh4AACAASURBVBfB0OCanGEYmKZJT3cC1/N4dMdWKgqLCNn9zysIBIiFQjy6Y5sfkce1PQdaiRaFB20rKgjS3tlHKp09zlEiIv47s+xSglaYrkwLvdkOrFAfZCMkmqcOPKcvmSYUsCkq2UjG7aMwUEPIKqUwUI3jptjd8+hRr9vW08e+lg5SGf0NFBHJVYZhsLz8KlzPoSvTQk+mg3BhCjdRSrr9nSJPV1+C4sIQmdBTABTYVf3thF1D0mnnYO9Tg17X8zyaOns50NpJxnEQkaFTT54cMXVaJW+8un/QNsdxwfOoqIyScR16UilqI4PnRiiwAzT39Y5mVAGqyqMcau6iOFAwsC2VzlJYECQY0K+diIwtaTfF/uweWpoPURaq4JLqm2lM7qYr00JZcAJnhyr46d5Xj7QnHgXBAF+4fDnNzl2ErNJBrxWySmlLvjkwUWdfMs1/PLORN/Y1YpoGtmVy9fLTWTFvmj8nKyIiH1jCSbA7u4OW5kNUh2u5vPavaEhspy/bRXV4Kgsp4GcHXqe7rxcPj9KiAv7qskXsTf+BAnvwarkhs4SWxGvMKF4FQEdvgh8/9TK7m9oxgIJgkNUXLGHR1Ak+nKlI7tOnzRyxaMkUnn9mK81N3RSXFJDNunR3JVh54XyisQI8z6MuGqMrlSQWeqcHSVcqyfxKTfY72i45dy73/Ow5ArZFYUGQVDpLe2cfn7hkIabp31Ct3mwPW7vfpCPdTm1BHbMicwhZ4fc/UETyVm+2h18f/DkN2YMUdxfjeA5FdoSrJ36KObGl/U+Kwv/8bC17mtoBmFZdRsC2aG8sxPWymMY7bydcstjGO39XHnx2M2/sa6S6JIJhGKQzWX727GaqiyPMnlA5qucqIiIfXHu6jV8d/Dmt2WaKu4t5tWsT5cFyVk28gQKrf26dybNgwZQ69jZ1ELBNplaVYZgO+w/beDgYvLudyBA0+4dqeZ7HPWtfoqG9i+ri/nYikcpw75Mvc/s1F1JbqjneRD4oDdfKEYVFIW77m4v50IrZeB5EowVc++nlXHblYqC/6+QNp51OXzpNWzxOMpul5UgPnk/Ome9n9HFpzvRqbrp6GbZt0tTaQzqT5ROXLGTl2bN8y9SSaubBfT/hxbbn2NW7naeb1/KLA/fTl+3zLdPbPC+F5zTheSm/o4iMOy+3vUh3pouoGaM4UEJZsJxENsHzLc8Mel7AtphdV8nsukoCtgVAXWQlKacdz3MB8DyXZLaVuqKVGIZBdzzJq3sPUXWkwAP9c5QFbZs/vbl7VM9TRESG5tmWp8i6mYF2ojxYTnu6jY3tLw96XkEwwLxJVcysrcC2TCwjQE3hMpLZFjzPA8D1HNJONxOLVgLQ0NbFgbZOKmNFA+1EQSiAh8f67QdG90RF8oR68uSQWHEhV37iTK78xJnH3H96VQ1fP+8CfrdjGwd7ujmzto4rZ81hYkyTmo2mw109tPb1UTeplG+suYxkKkswaPm+nP0zzevwPI+yYPnAtvZ0G5s61rOi8kJfMnmei5t8DCfxOHhZDCOAWXAlZvijmpxaZJTs6N1K1I7RQ8/Atlggxu6+Hbiei2kc/29XXdFKEtlmDsdfwsDEw6Wm8BwmRS8BIJ7OYADme36fg7ZFVzw5IucjIiLDJ+OmORDfR2mgjE46B7ZH7Cjbe9/ivMoLTnj8tNhVpN1uWpNvYGACHpMiF1NdeDbQ306YhnHU+z7btOiKJ4b7dETGBRV58syssnK+dM6H/I4xLiUzWe59YQOvNzRiGQZJJ0NFaYSSSAFVRREunj6d6WVlvmRLuykakw2UBgZ//YgdZUfvNt+KPG7qaZz4r8CqwTACeF4aJ/4QGBGs8AW+ZBIZbwKmjYs7aJvrudiGjXHUQrmDmYbN7JJPMTlyKUmnjbBVRth+p5BcES0iEg4RT2UoDAUGtvcmUlyyyL+ejSIicnJMw8Q0zGO2E0Er9L7H22aY08r+kkS2hZTTeWQC5nduQNeVFfcP5c06BI/0EvU8j1Qmy2mTqo/3siJyAhquJTJMfvvGW7x68BA1sQjFRWEOpHr44949vH7oMK80HOSOZ5/hlYYGX7KZWJiGdVQD7XgOYdO/OXncxONglmMY/R/+DCMIZhlu8ne+ZRIZb04vXkJ3pmugK73neXRlOzmteNFJ96gL22WUhGYNKvAA2JbJp1cspieRpKWrl654ksMd3dSURTl37tThPhURERlmlmEzN3oaXemOd7UTLr3ZHhYWLznp1ymwKykJzTpq2fSicJCrly2grSdOa3cfnX0JDnf0MHtCpSZeFhmiU+rJs337dtasWcPNN9/MjTfeOFyZRHKO63n8acdeqqL980409PWQcrIUh8K0x5PMqqwgnslw/+uvsri2FnuUh27Zps286AK2dL9KWaAcwzBwPZe+bC/Lys8b1Sxv8zwPz+0Aq2bwDiMMbqsvmUTGoyUlS2lNtfBq30aMtIGHy9TC6SwrP3dYXn/RtAn8/aoP83z9Xtp6+pg/qZplsydTGAoOy+uLiMjIOrfiAroynWzrq8dIg4fH/OLTWVC8aFhe/4IFM6grL+bFbfvoTaZYPLWOs2bWDcz/JiIfzJCLPPF4nDvuuIPly5cPZx6RnOS4LhnHGZh3py0ZJ2BamIZB1u3vPVMYCNDY20tbPE51JDLqGc+rXEmf08vevt2YhoHreSwpPYv5sdOH/Jqu57GlqYlXDx8mbNucM2nSSR9rGAZmYA6usw+Mdw0jczsw7HlDziQiH4xt2lxeexVl7VVU1lYQDcSoCFYO67xYkypK+NSKxcP2eiIiMnrCVphP1l3PS10vUF1bTWmwjNLg8E5BMKu2glm1FcP6miLj1ZCLPMFgkHvvvZd77713OPOMa4d2N/Hn32zg0O5mJs6u5byPL6V6iv7Y5YKAZXFabRXbmlupjBQRsiz6shmyTpbaWBToLwRh9Bd7/BA0Q3xswira0230ZXspDZYRsaNDfj3X8/jxK6/w5/37CVgWnufxhx07uKC8nHnzTq5IYxZeh9t9J57TCEYUvF7Awiq8esi5RGRoYmYx0yMz/Y4hIiJjkGEYlJhlaidEcsCQx4zYtk047N9cHvlmX30D9/zdA2x5YTuJviSv/ameH/7d/TTsavI7mpyk689YSNi2OdzVQ9QMEk+nsU2TyaUluJ5HY18vyyZOIhp6/0nqRlJZsJxJhVNOqcADsLWlhRcOHKA2GqWqqIjqSITywkJ+f+AAPamTWwrdtKcTiH0LM3QehlmMGVpBoPhbGPbUU8omIiIiIiIyHo3o6lr19fUj+fIjJplMjnr2R773JIlUgqKSApLpBGYYetp7+fndj3DFmpWjmuVY/LgmueC91+XTMyexpaWdlniCGbFCtvd0cqC1BQ9YWFbG0lA4b67jEwcOkOjro9txBm3PZrM8tWkTc0pKPsCrLTvyD6DryL/8od8fEREREREZDSNa5DnZIRtjTX19/ahmd12X3pbHqJtaO2gOhFg0Rldj75i4jqN9TXLFsa7L0nf9P+04tPT1EQ0GieVZz7edhsHrvb2URAf3CGpNJJgzcybzKit9Sjb2vPfnZOPGjT6mERERERGRfDWiRR45OYZhEC2NkEqkCRe+M5QnlUhTWhnzMZmcqqBlURfLz+/hWXV1/La+nmQ2S9ju/1PSmUgQDQaZVV7+PkeLiF96Mr1s7nyLhkQT1aEKlpTOpzRY/P4HiojIuNCe7mRTx5u0pNqZXFjLopL5ROxCv2OJyEkacpFny5Yt3HXXXTQ0NGDbNmvXruUHP/gBJR9oiIZAf5Hnw9ct47c/fILy2lICoQDpZIbutl4uu/kCv+OJHFNtNMptS5fyk02b6Eom8YCyggKuqasb9SXiReTktKc7+emeX5F0koSsILt79/NKx+t8duoqv6OJiMgY0JBo4oF9v8HxHIJmgF29+3i5/XVumXqN39FE5CQNucizYMEC7r///uHMMq6dffliUok0f/rlS2QzvQRCAa689SIWXzDf72i+8rwsvYmn6Us+DWQpCJ1HtOAjmKbuJowFSydOZEF1NXs6OghYFtNLS9m+bZvfsUTkOJ5pXk/KTVEeKgUgYhfRlenhycbnOYu5PqcTERE/eZ7HHw7/CROD4mD/jfuIXURbqoPnWzcygxqfE4rIydBwrTHCNE1WXrOM5R87k3hXnKKSIgLB8f3t8TyP9p5/JZ58DsssBUy6+35BMv0qVSXfwDDy9/p0pjvpzHRSHCimNFjqd5wTKggEmF9V5XcMETkJO3v3EXvPynoxO8LeeANLmO1TKhERGQvSbobDyWbK3/PeMxaIsL13t4o8Ijkifz8l56hgKECwSnMjAGScAyRSL2BbEzGM/uE/hlFIOrODZPp1CkJn+Jxw+GXdLOua1/FW91uYmDiew5zoHC6tuZSAGfA7nojksJ7uBEbKJBVMYwcLBrZnvSxhM4TpGic4WkRE8l1vVxIn5ZExMwQDwYHtGTdLkV0IzgkOFpExQ0UeGbOy2YN4GAMFHuDI6mMG6eyevCzybOrcxJauLZQHyzEMA8/z2NqzlZJACedVnud3vA+kLXWYvX1byHppJhXOoSY8HdPQXD0iQ+W5vSQTvyabehYAO3geocKrMc3oCY9Lp7P818Mb2PTybvpqk7TPPsTk8lrqJpTh4tGR7uaCynMw2lTkERHJZa7TRir+SzLplzCMEIHQRYQKr8IwTrzCa7wvxa9/9hJbtxykc3qG3ZN3MLN6IpXVxTieQ2+2j4uqPwSHR+lEROSUqMgzgjzPw8PTB9shMs0SjvWRwzA8bDM/l+fe3LGZWCB2pJjVX9QqCZTwauernFtx7sD2sW57zwZebnscAwMDk+09G5hRtJjlFR/PmXMQGUs8zyHecxdOdg+G2T88MpNah+vsojD2bQzDOu6xT/7Xa7zy4k4qq2NUOFECrbAvc4hsME0kFuasstP5UMWZ7GjbPlqnIyIiw8xz48S7/weu24ZhVgIOqcRvcZ0GCqJfOuH7r7cLPBVVUcrjEfZ3GOxwDpIJpQgXBllZeQ4Li+ey9fDW0TshERkyFXlGQNrN8ELrS7za+ToZN8OMyHQ+XHU+pUGtPPZBhAJzsa1JZJ2DWGY1YOC4rZhmMQWhs/yONyJSbooiu2jQNtMwSXtpvP5+TT4lO3lpL8GWtj8QsUuwjP4hZp7nsrvvVaZHF1MTnupvQJEc5GTrcbJ7McwJ7xSBrTqc7F6czFvYwdOPeVw6neXlP2+nvDKKeWTVu7qWKRTtKyPSFuK2v7pcy+KKiOSBTHoDjtuCZdUd2WJjWnVkM5twnYNY9qRjHtfVGWfrloOUV0YxDAPDM5jaOJPC7eVMyVbx6WsvoMA6cU8gERlb1MVkBPzu0O95uf0VCq0CSoMl7O3bx3/uf4hENuF3tJxiGCaVJV+jIHgmjttI1j1EMDCDyuJv5O3qWrMjs+nJ9Aza1pPpYUbRDA52dLNxfwMHOjrxPM+nhO+vmxbAGyjwQP/30sDicGKXf8FEcpjrNOF57lF3Yj3Pw3WbjntcJu3gZF0sa3BzX2CGcZssFXhERPKE4xzAeM/9+/42w8R1m497XCKexjQNTHNw+1JIGK/ZUoFHJAepJ88wa021sbN3D+XBsoE34yXBYtpS7Wzt2c6S0kU+J8wtlllCefGXcN044GKaEb8jjajlFcvZH99Pe6od27TJullCZpjtOwp5rOGPmAa4wMIJ1dx23tmE7LH3K2xx7GEjHi4BI3jMfSJyYqZZNWh+sgGGgWkef3W7wqIgldXF9HbHicTemWy5uyvBOSu0mpaISL6wrEmk3zMzcv9NQfeE7UR5ZZRgKEAqmSEUfucGXTyeZu7pE0cqroiMoLH3CTHHdWe6MQ3jqLuttmnRkmr1KVXuG86eO67bfzf83d+jRDpDfWMLacdhVmU55RF/7m4XB4pZPXU1W7u30pxqpiJYwfa9HpsO7mdCcXRgMuZXDzbyuy3bWLX4NF9ynkgxNYStIhJODwVW/4SwGTeFgcHkovk+p5PhsmXLFtasWcOUKVMAmD17Nt/85jcH9m/evJm77rqLVCrFJZdcwpo1a/yKmheswHwse+qgOXk8txnLmooVOP7vlWEYfOzapdz3w6dItvQQDgdIxNNEYgWsuFC/jyIyctROjK5AcCmpxCO4TiOGWQE4uE4LgeCZmNbxizWBgMXHrl3KL//jz1h9KQIBi3hfmuraEs48Z8bonYCIDBsVeYZZSbAEz3PxPG9QESHrOlSHj19Fl5F3aH8bax/ewK76wxRGQpz3kQWce8lp7Gnv5Ad/fJFEOkP/lDcGqxbP57IF/tzlLrAKWFK6ZODxfeseozJSNGgy5spIIX/auWdMFnlMw+LD1Z/hmeb/pDvTChhYhs15ldcQC5T7HU+GSTwe59JLL+X2228/5v6///u/57777qO6uprrr7+eK6+8ksmTJ49yyvxhGBYF0a+Siv+KbPr5/p5xoYsJFV6NYZy4KZ8+q5q//soVvPznHTQ3djF9Vg1nLZ9B9F09e0REhpvaidFlmIUUxb5xZHWt9RhGkFDBx4+srnXiOR0XnTmVsvIIL7+wg66OOHPmT+CMc2ZQUKge2CK5SEWeYVYWLGVebC5but4iFohhGSZdmW6KAzHmRNU13i/tzd38+P/7PZ7nUVlTTCaT5Q+/2kBHZx/PWO2YhkFN8ZFeJ47Drza/yZyaSqZVlPqa2/M8Mo6D9Z5x0pZpks46xznKf2XBGj5e90XaUg24nkN5aAIBM+R3LBlGfX19x9134MABiouLqa2tBeCCCy7g+eef59Of/vRoxctLphmlIHIzcPMHPra6toSPXbN0uCOJiByX2onRZ1oVFES/QAFf+MDHTppawaSpFSOQSkRGm4o8I+DSmospD5WzueM1Ek6S00tO49zyZYQtfcj1y8vPbiOTzlJRUwxAMBSgsqaEp/78Fn1LS6grLR54bsCyMA3YtL/B9yKPYRicNWUiL+89SE3snfmIWnv7WDZtbN/tsgyLqvDYzihDF4/H2bhxI7fccguZTIa//uu/Zvny5QA0NzdTVlY28Nzy8nKam48/6aPkBs/zeGPbIZ5+aTud3XFmT6viknPnUlkW9TvacWUch46eBEXhIEVh3ZEWGU1qJ8Yf1/XY8MY+nn15J32JFAvn1nHR8jkUR8duz9FUJktnb4JYUZiCYOD9DxDJASryjADbtFlWvpRl5bprOlYc3t9G+D1dTi3LBAOy6WP1iDFwXHd0wr2PVYvms7OljUNd3dimieN6lEcK+cSi/JhPI5XJsr+lk4BtMbmi5KjVHWRsmjt3LrfddhuXXnop+/bt4+abb2bt2rUEg0ECgcFvkt47fPXd6uvrh/T1k8nkkI8dbbmS9f1yvrq1iadf3kdByCYYMHl2fRsvbtzOZ644jeLo6N7EOJlrumV/K09tOXCk16PB6ZPLuWjBZAL26C0smivfe8idrLmSE3Ir60hQO3FyciUnvH/WZzceYMOWQ0QKg9iWwR/+1MqfN9TzmY8uoCA0eh87T+aaep7HyzsbeWHbYRzXwzDgrBnVrJhbN6rvRXPl+58rOSF3so5kThV5ZFyYOL2SPdsOD1pdxsk6xLIW2YIgiXRmoHrvuC6O57J40gS/4g5SVlTIt664kFcPHOZAZxeTSotZPLGWgkDu323YtKuBB57ZRDrjAB7lsSI+f9kyastifkeT9zFjxgxmzOifkHHKlClUVFTQ1NTEpEmTqKqqoq2tbeC5ra2tVFUde06yefPmDenr19fXD/nY0ZYrWU+UM53Jcv/jO5hcV0Uw2P/WoRJobuuhsctg2dmje37vd023H2zhT9vrqSgrJRwM4LguO1t7qW1Nc8OHlxz3uNHOOZbkStZcyQmnlnXjxo3DnGb0qZ04ObmSE06ctbs3yY7f1DN9Sm3/jVT624mm1m76MgWcsXjmmMj5tpe37mf9ng5qqioI2hZZx+X1hh5mTLW55MzRm2IjV77/uZITcifrqeY8UTsxerezRHzieR6Riih723v586t72ba3hfbOOC2NXay8ZAGfv+AcetNpDnV1c7irh+aeXi6ZN4tZVWNnkuCCQIDl0ydz3Rmns3za5Lwo8DR19vLTdRsIB2yqSiJUlUTpjqf4l8dfJOuMjV5UcnyPPPII9913HwBtbW20tbVRXV0NQE1NDdlslkOHDuE4Dn/84x85//zzfUwrp6qrJ0k6kx0o8LwtUhhiz8G24xw1chpaevi3X73I//jRWv7z9xtpausZtP+Pr+4kGLAJHyneW6ZJVUmEF9/aRyKVGfW8IuOR2onxpaW9F8MwBgo8bwsFbfY0jG474Xkeb+1q5P/+/Dn+x4/W8shTr9HRHR/0nCc3bae4KEzQtgCwLZPyWCFPbtp+ZOl5kdylnjyS9158cSe/eXQTk2ZW09bURXNrLx29SW656TwuunIxpmnyPz/xEV4/eJhU1mFOdSWTy4rfdyUCOTWbdx3Edb2BD2EApZECmjp72NPUzqwJmvxvLLv44ov5yle+whNPPEE2m+Vb3/oW//Vf/0U0GuWSSy7h61//OmvWrMEwDK666qqByTUlN0UKQxiGQdZxsd/1Bj6RTDNn+uiuHLllx2F+vm4r5aXFFIQDbHzzAK9ua+DLN15ATUV/L8D2njjhwOC3OJZp4gHxVJqCUO4XykXGOrUT40txNIx7jBWG05ks1eWj20P7tZ0tvFRfT2E4QChg8+ym3Wze2sD/89kPD8wP1NmbOGqutqBt0dGTIOu6BCxrVDOLDCcVeSSvZTIOTzzxBmVlRQSDNuWV/ROEtrb00Od6mGb/h5XSwgJWzp7uZ9Rxpy+ZxjjGmGeD/nl6ZGyLRqPcc889x92/dOlSfvOb34xiIhlJBeEAK86aydMvbqOiNIJtm/TGUziux/lLR68Lvud5PPL0axSGA5TGCgEIBwO0dvbx5EvbWH1l/1x486dUs27TDgrf9QY+nsoQLQhREhm7E4CK5BO1E+NLRWmEhXPq2FzfQGVZBMs06OpJEAzYLF04ZdRypDNZnnvtADWV5QSPFPvDoQBNbT288NoeLj+vf07LOZOq2LKnkYriooFju+NJplSXqMAjOU/DtSSvdXcnSKePHmJQFAmxf1+rT6kEYP7kahzHHdQlNpN1MAyDKVX+rmomIke74oLTuOz8+fQlUjS39RAtCnPrDecysebEv68pJ0V7up2Me+rDpOLJDO1d8aMm8IwVhdi5v2Xg8cqFM4gVhmls76Yvmaatu4/uvgTXnL8Qy9RbHxGRkXDDlWdx/tIZdHUnaG7roaYyxprPnE9ZceEJj0s4CTrSHWTdU7/J19YVx3G8gQLP24oKgmzf9047ccXZ87Atk5bOXvqSaVq6eklnHa5esfCUM4j4TT15JK9FIiEs0ySbdbDtd6ryiUSGGTOqfUwmc+qqOGPmRDbuPEjItnA8D8d1uWHFIqIFo7tSj4i8P9syuez8+Vx87lwyGYdwyB7UJT/jOGxpbmJfZydVRREW1VSzsWs9mzs343kefakshckpTDBns3TKJKZXlJ3gqx1bKGgTCtqk3zOvTiKVYUJVycDjkkgBX7nuAp7bsput+5upKK5k5cLpTK8dO3OtiYjkm1DQZtVHFnPVhaeTdVzC7xkam8pm2Xz4MI29PUwsLmZuRRkvtD/HW91v4XoeybRHQXwmk0MzWDZ1EnUlH3yYV7QwhEf/QirvLuon01mqyiIDjyeUx/jaDR/mmdd2sedwOwum1vDhxTOYUF485PMXGStU5JG8FgoFOPe82fz/7N13fBzXeej935mZ7R29EoW9N7GoUpSoasmqlmQ5ThSXxOlxEudz3+Tm3tfX8Wsn17GdG18ncYkT9ybLRVaj1SiKIkVRFMUCVoAAQfSyi+07O3PeP0CBgggSBLkkAOJ8/+NgZ+ZZYDln9pnnPOfFFw4QKfLhcOgkEllsy+b66y9f53zlTJom+Mimq1g3t5a3WjpwOw3WzptFvariUZQpzdC1UX15AJK5HF94dSst0SiaACnBG+qhujxGuaeE5r4oHUMxhGMn+wdibD54jIdWLeXWhXMnfO6b1s3lR0+9TiRs4TB00lmTVMZk07rR1/Sw38Pd6xdz9/rFF/2eFUVRlPNnGPqoh6sA/akUn9/6Cn3JJEIMT78NFXdSWZqmxFXMwa5e+lJxhPEq+08M8uyBw3zs2jWsrauZ0Ln9XheLG4pp7kpQGvFj6BrJdBbblly/avao15aG/HzghuUX/X4VZapRSR7linfLLUtwuQy2bDlILJqivCLE3b91DdXVE3+KrBSWrmksa6hkWYNqtqgo09kzR4/QEh2kwh9gMJUmZ+eJi+P0xIP4tTydsSG8TjdSaGhFPQS0Wn66ez9X1dVQ5D3dI0fKPCAR4uyNkTetW0B7eweHTiYxTQuf18lv3bWGhY0Vl+GdKoqiKBfix/v30Z9KUebzMZhKY5Kj327DmyxFt9L0JVP4nB4sTeAsGsAVK+fbO3azvLoCl3H6K+vwOAFCnP1r7MZVs6jtsdj2VguWLSkOeXn0zquoKQ+fdR9FuZKoJI9yxdN1jY0bF7Fhw0LyeQuHQ59xK2dJmQMMhFC9KBRFKbxtJ9rwGg7eaGsnk7cQWFQGMrRHIWS4QQgEgDSwtSwOXUciOdbbT1FdDbadIp76IZnMy0hp4nIuJ+D7MIZRdca5NE1w9ZIqPnzfPFKZHH6vq2B9dvKWzatHW9jX30VFOMCNDbMp9vjG31FRFEU5K1tKdp48iUfXeb21HdOy0Y0sZX6T5oEodhCMU9dxIXUsPYPbYRDLZGgdiDKvrATLHiSR+D6Z7HZA4nKtI+D7ELp+5kNbh6Fz/81LeN/1i8nkTAJeN9oYi31ciGzO5MUjRzkWG6C+NMIN9bMJOFSbAWVqUUkeZcbQNHFGA+YrnWkeI578DjnzMEK48XruwO+995xPyRVFIWu3pwAAIABJREFUUSbK0DSO9Q+Qy9t4HQ7AwM77sESaeCY38jpby+IyS4DhlfRchoGUktjQl8mae9H1CkAjZx5gIPYZisP/QFNzgm27W8hkTZYvrGHdqVVaHIZOqIArZfXHkvzFz3/JQauHd9rBf33fDj6z4XbWlNcW7DyKoigzjQA0IWjq7kMCXufwOCGkQdbOkrPy2KcW4pBaDmemEikltpSnxok8g7HPYeU70PQyALLZ18lbbYSDf89bTV3s2NuKbUvWLq3Dq9nA6T5uhdLeG+XPfvlzTojY8Ps6CBV7d/CFm+5ibri0YOdRlIulHuvPUIlYiv2vH6NpVwuZVG78HZRpJ291MRD7LGa+DV2vQtMCJFOPM5T89mSHdkEsO4tlZyc7DEVRxrCuqob+ZArXSA8GwUBvKR6HRkrGQeTJigQCDW+mgaF0Bq/LyYLyEvJWG1lzP7pejRDDFYe6XoZtD/Hqmz/h6z/dRvPJfnoGE/xs81v82w+3krfsgr+Hrz77KgetXsKGh2LDS5HhJRHL8o+vv0Q6f/ErgymKosxUQgiWlpURz2ZxnKrYkRL6e8rxOiFHGluYmCKJZrvwZGvoT6WoDAaYFQmRM/eRz7ejG5UIoSOEjm5UkM938NTLj/OdX+7kZHeMrr4hvv/kGzz16rFRq7cWgm1L/uHJFzipDVF0apyIGF56+xN8/vUXsezCj0uKcqFmVlmDAsDuLQf5xTdewLYkUoLL7eCRT97OnKWzJjs0pYDS6edBmujGO30qnOh6FZn0i/i9D6Br02Necibfz9HY4wxk9wOCYvdS5oQewKVPj/gVZSbYUF/PV52vk7LM4WlZCIIiQiRejjvcz8IKJwda0+QT5fTlJUG3zh9tWI/TMMhk+xBoZ0yjzVuCo217KS26Y6TRs8/j5HjHAMfKHCxdUrj446kMb/aexBnQ0UbeAbh1B71DCQ7HellefObUMUVRFOX83D57Lk/sbSJtnU6aF9sV+KLlRCoS1JUKDreZ5BLl9No5ygJ+/mjDeoQQWFb/mMfM5HIcP3mY8pJrRqZj+b0ujrZ20tLeT2NtScHi7+wf4miuH7fHQLxrnHAJgxODUdqTMeoCavEQZWpQSZ4ZZqA7xhNfe55gkR/nqWUN04kMP/jSM3zqX34Ht0/NKb3cchmTXS/sY/dLTeiGxlWblrBiwyJ0/eyFdrYtaeuLks6ZzCoJ43M7z3hN3mpDaO5R24TQQQhsa2BaJHksmWNP/1fIWjHc+nAZbH9mL+l8N6tK/xrtHE33FEW5fIp9Pm6pb+RATy9up4FLNwg6nHQMxXlw0Z1snNdIdn6elr5BdE3QUFI00n/B0CuR2Ehpj+oblslmiCXKRq3kJYTAYeic6IoXNH7blozZreHUSmHa2D9VFEVRztPc0hLWlVXTm05iGDpew4HPcNA5lODBuk0sr64kuSBHa38Ul8OgoTiCdir5b+iVgEBKOfJAQEpJNmsRT0XQ9dPX6Hd+fqJrsKBJHtu2xxwLhAAJ6DOs36cytanpWjPMwTePY1tyJMED4PG7MbMmzQfaJzGymcmybL73D7/kV994kWhfnL7OKI9/5Tl+/q+bz7pP71CCv3/8ef7xFy/xlWe28d++9zRbDjSf8TqHYx62TI/aNrwigUA/NZ95qhvINJHJ9+MxShBCQwgNj1FGKt9DNHtkssNTFOVdHlu/mnKfH9uUJNJZuuJJVtZUcd3s4R46LsNgQUUpc8tKRhI8AIZRhcd1DZZ1EttOImWWfP4khl5BR2/DGSX3lmUT8J2Z2L4YQZ+bJeEKTMvC4nTJfTqfoyzoY57qtaAoinJRNCH4xPXrCDhc2KZNPJWlO55k49wGllYNV537nE4WVZYxu6RoJMED4HAswOlYgGW1Y8s0tsxgWScR2lz6B8eusgz43GNuv1CVJSFm6WGytoXN6XEpLfPURyJU+UIFPZ+iXAz1GHyGyZv5MbdLCVZezSW93Jr3tnF07wnKaotHnjx4Ax52v9zEde+/ivJZxaNeL6Xka5tfp28oSXkoAEAub/H9rW9RUxymsfz0CgMe10ZS6c3krS50rQgpc9j2AD7vg2ia//K9yYuQtQaRnDmnWiLJ2bFJiEhRlLMpD/j5+7s2sa+zh1g6Q004yJzS4vNazTAY+D0Mo55UZjNSZvB6bqOk6P1UleymvSdKScSPEIJEKouhayxsKB73mBMhhOAPbruW1l910iL6yJoOJBohn5u/u3oTLl3dLimKolyshuIIn3v/bezt6CJtmjQWF1EbCY07TgihEQ7+Jcn0r8lkXgZsfN77iITvJBx8hYFokkjIC0AsnsbrdrCwseKcx5woQ9f4i9tu4G83P06nHiWXcwGCsqCfv1l/86iklKJMNnXXMsPMWTaL537wGlbeQj/VINPM5tF0Qf3C6kmObuZpP9qNEIwa3N6ZU9zV2ntGkufkwBAnB2KUBU8naZyGjqFpbD/cNirJo+tFFIU/TTL5ONncbjQthN//MB73hkv8rgrH56hECO2M8lyQeI3yyQ1OUZQzOA2DVbUT710jhAOf9334vO8btf0jD17ND5/axaHmHoSASMjL7963nlyit1AhA5C2Uuwxn+aa6ztZmMyQzFo0uK7hAws3EXAW9mmwoijKTOZ1OlhXP/EVCzXNS8D3AQK+D4za/olHruP7T75BW+cASKgqC7Hu6ho87sKuJDtkRjmgPc1N1w8wkEiRMXUW+m7kvvnX4zbUqrXK1KKSPDNMZV0JG+9fw0tP7EQCAoEQcM/HNxIIeyc7vBknVBJgjEIVhBD4x/h75PJ5hBBnPPHQNY1U9sxV0gy9nFDwDwsW7+UWcs4h5Gwkmj060mg5aw1S7F5CwFE/ucEpinLJhfwefv+h64jF0+RMi+KwD00TNDUVNsnzYs8v6Ei3UuQsodglyNlZUtY+svIqAhT2abCiKIpSOGVFAf7swzcyOJQGKYmEvBw8eLCg57ClzbNdPyKej1HsKqHELUhbKTJyFxZXASrJo0wtKskzwwghuOnBtSxc08iRPW0Yhsb8VQ2UVE79JrxXooVXNeILeoj2xQkV+0HCYE+M4srwmJVVNcUhnIZOJmfidg4PKFJKMmaeFQ1X3sovmtBZUvT7nEy8TFd6OwJBY+heqn03nNcUEEVRrgyhgOeSHTtmDtCRPk7IKBq5rjg1F2k7xaH4HkpcKsmjKIoylQkhKApduofV3Zl2YuYgYce72iLoXqJmP82JJpaG112ycyvKhVBJnhlICEFVfSlV9aqR5GTz+N387v/7AE98dTMnj3UDMHvZLO77xKaR6XTv5jQMPnzDKr7x/OvE0hl0TcPMWyydVcHy+srLHf5lYWhu6oK3URe8bbJDURTlCpS1MqeqWkcnjg0MEvmhSYpKURRFmSqydmbMNRYFgqSVuOzxKMp4VJJHUSZZxawSPvG5R4gPJtF0Df84TyJWNVbzd5Gb2XHkBIlMjiW15SyZVTFqmWFFUZQrTdbM0x9PEfS6CnrciLMEXRiYtolDO11yn7OzzPLOLui5FEVRlEsnlTWJJtNkzrLQzIUqcVUgAVtaaGL4IayUEhuLKk9dQc+lKIWgkjyKMgUIIQgWnf+KV5WRIPeuXXzJ4smZeTRNU4kjRVEmnZSSl/c38/OdBzAtCyTMDruZM3cejjEqHifKoTlZX7yJV3qfwhAGumaQtTMUu8qZ7b9011lFURSlMGxb8uSuJja/fQRbSpKJJPdlde5evXBkQZOL4TeCrAhfzZuDW3FqLjQ0MnaaWu9sqj0NBXgHilJYUzLJk7XyGJqGLtQXTEWRUpLPHyCbfR2BhtO1HsOYd0l60nT1DfHEb/Zw+HgPhqGzdmkdd21YUvAVChRFUc7X3rYufvDqHkoCXpyGB8u22dXWxS927ufBq5cV5BwLgisIO4tpGtpNKp+gzjePeYGlOLXCVg0piqIohbelqZkndzVRHgpg6Br9+Sy/3tVE0ONi45LCVGSujtxAubuGQ/E9mHaORt9CZvsXo4uLf9igKIU2pZI8zfE+ftC8i+Z4Py7NYFPVPO6etRSHpv7zKDOTlJJU8rtkMk8z3Llfks48i9fzAF7fAwU9VzyZ4Svf20LOzFNWHMCyJdvebGYgmuT3HrpWNTpWFGVSbH77CD6XE6cxfMuiaxrFPhcvH2jh/WsWjWy/WBXuWircE1/WV1EURZlcz711hCK/d6QCXdc0irxenttzuGBJHiEEtd7Z1KppvMo0MGWSPN3pOF/Y+zya0Kj0BDGlzZMn9pPI5/jtOWsnO7wZIZ012d/aRSKdpbYsQmNF0bT4Ym9ZNltfPcy2bUdIZ0yWLK5m06YlFEV8kx3aRbOsVjKZZ9C0SsTIHOA86fQTuNzXoevlBTvX7qZ2UpkcZcUBAAxdUFYS4FBLD119Q1SWhgp2LkVRlPMVTWRwvWdaliYEWcsmY+YLluRRFEVRpqdoKkNpYHRPS5fDoCeWQEo5Lb7PKEohTZk7o5c6j5CXNuXu4b4kTqFT4Q3ySvcx7pm1lJDz0i2fqkB7X5R/+eWrJNJZpAQhYNXsGn7nlqumXF+WrGXy1kA7R+M9lLuDdG4fZO/rJwiHvfj9LnbvaePo0W7+7E9vw+cbv9ReSklPJkbGMqn0RnBqU+a/BaZ5EIkcSfAACGEAkrx5qKBJnu7+OPp7/tZCCIQGg0NpleRRFGVSLJ5VzpYDzbidp6eNps085SVhAm41nUpRFGWmW1hdypHOforflegZTKRZWFOqEjzKjDRlvs2eTEVx66P7fuhCQ0MQzaVVkucSklLyX5vfwMrbVEaCI9veONLO0oYK1s6fNckRnpY0s/zTgc2cTEZxaDrpXI7WaB/XVDXitoc/P6UlAXp6htj9VivXXTvvnMeL5pL8V/PLtCR6EAicmsFDdetZXTw1SjGFcCPOsmgjwl3Qc9VVFrFtd/OobbYtkTaUTaAptKIoSiHdsmwubzafpCsax+dykjFNMqbNw9cuVzfviqIoCveuW8wXfrGFnlgCr8vBQDJDOOTivrVLJjs0RZkUU6ZEY06wlHQ+N2pb3rYQAopd03/azVTWN5SkczBOyHc6aSCEwO92sr2pbRIjO9PzXQdpTw1S6Q1R4vYTwoMU0BTuRiJHXud0GrS3D5zzWFJKvnXsJVqTvZS5gpS5g3h0B99peYX2VP+lfivnxelcATix7cTINtseQggPDkdhB65l86sojfjp7hsim8uTyuTo6ouxdlkdJRGV5FEUZXIUB7z8zf0buWPlfMrDftbNncVj1yxkcW3hKhkVRVGU6au2OMzfPnATGxY3UBbys7qujL+5/yZqS8KTHZqiTIopU8lzfflsXuw8QldqiCKXl5xtEc2luHfWcvwOVY59KQkE78qPvItEmzJpwGFv9B0n7Dhdiul0GThMjZgrjSksnHL4I53L5amsPPeFvSsTHUnwvPM02KU7EHnB9r4jPDir+NK9kfOkaWECwb8gEf8KltV5alsAf+Av0TTvOHtPjNvl4I8/tIHntx9id1M7bqfBg7eu5JqVjQU9z2SQUtIxOEQub1FTHMKhq2buijKdhH0e3r9m0ci/m5qaJjEaRVEUZaopC/l56JrlwPAYUR5WDyiVmWvKJHkiLi//z7JbePLEft4ePEnQ4ebB+hVcU9Yw2aFd8YqDXmpKQvTEEhT5hxMHtpQkMznWL6yb5OhGc+sOku+q+HK7HBQV++mMR8mbFoamE40m8XqdrFpZf85jZSxzuOfMe8r9HUJnyExfivDPW7Q/QcvBTnRDY/aiuUSK/oV8/higYRizT/XlKbyg3819m5Zz36bll+T4k6EnluBrz+2gY3AIIQQep4PHNq5myayKyQ5NUZRLSEqJJbNowoGmlrhVFEVR3kNKm7zMYggXQkyxJ9uKchGmTJIHoMwT4CPz1k92GDOOEILHbl3DV365la7B+KmiHsk1ixpYNbtmkqMb7caKeXzr6DZ8hhNNaEgp8Ve6ucpdj9lqkcjGWbCgkjtvX04gcO6eNZWeCIbQyVomrlP9oKSUZKwcS0OTt4zu6y8c4Fff3QZSAgLDqfPIH97M/OULz2t/KSWDuRZ6MwcxhINyzzL8jpk5rcGybf7v09uIJTOUh/wIIUhlTf792e38j4c2URpST3kU5XwMJ0wkxgTLO6XVCzIJehVCOAsWj5W32PHMHna9sB8ErL5pMatvWozhGL6t6U0f5GDsFyTzvRiahwb/jTQEblTJHkVRlEtESoktJfoExgkpJdjdIHOnxonCfTXNJLPseO5t9m49hNPtYN3ty1l67Ty0U/F1pN7kcOwpMlYMp+5jbuA2anzrVa835YowpZI8yuSpiAT4H4/ewsH2XpKZHLWlIaqLQ1PuQre+tJG25CAvdR1CIJBI5oXK+cSaG/Dd6UJK0LTzi9mtO3igdh0/bH0VLa/hEBppy6QxUMHyovpL+0bOorcjyq++u41wsR+Hc/i/ZzqV5cf/+gKf+uIHcXvPPXVRSsmB6M84kdyGQEMCR+LPsTT8ENW+NZfhHUwtLd0D9A4lqQgHRrZ5XQ6G0hl2Nbdz+8oFkxidokx9edvmqeZDPNNymKSZY15RKR9csIzGcNE595P2EDL5TTD3AxoIJ9L7KJrrmouOSUrJ5v/aQe+xGP7IcM++X/zb8xzd08ajn7qLmNnGrv5v4tS8+IwybGlyaOjX2OSZG7ztos+vKIqinJbJ5/n5kQO80HaMrG2xvLSCDy5YTqU/cM79pNWLTP475FsBAZoP6f0omvPie07mTYv//MzPOHGkC3/Eh91v86MvPcWJI13c9ZEb6UrtZc/Ad3HrYfyOMvJ2hn3RnyCERo1v3UWfX1Em24xO8phWjGh2FzmrD79jDgHXUjThGH/HK5TTYbCsoXKywzgnTWg80rCGTZUL6UhHCTu91HojI8moieak1pfOpdIbYXvvYeL5DEvDtawsapi0ZdQP7mkDyUiCB8DjdZGMpWlu6mTR6vpz7j+Ya+FEchs+o2yk7NSyc+yPPk6pexFOfWY1MU/n8mOuTaYJQTydG+MniqK8248P7eXp5sOUer0EnS7ahgb5/Osv8+lrNp3zBn44wXMAtIrhC7PMQPI/kHo5wri41QvbDnXSur+T+nm1I9d+b8DNwV1HaD/2I7K+H1Ir+jGZS5LZCM2JT5RwPP4yjf6N6FrhKooURVFmuq+//To7u05S5vGhaxoH+nv47PaX+Oz1txByjV1VL6WNTPwfsHpBKx8eJ+wkJL+C1D+D0EsvKqbW/Z2cONpFaU3RqHFi5+ZdrLujk6j8FrOESZY5pGQjhubGTZijQ5up9q6dcg+5FWWiZmySJ2W2cmzwn7BkCiENesVz+IzZNEb+fLJDU85DidtPibswU23qfCXU+UoKcqyLJW05XLr63u0w5vb36s0cRKCNmlesa06kZRHNHafMs7iQ4U55daVhQGBa1kizZSklectmYU3Z5AanKFNcPJflN61HqfD5R6ZpFbm9dKcSvNB2jA8tWjHmftLqO5XgKT+deRduwEBmX77oJE93Wx9SMuomXAjBsut3kssPkbeTaGj4ZRMuu4t+7QZ04cCWeUyZQkcleRRFUQqhIzHEru4OqnyBkWtyqcdHZzLOjs4T3Fo/d+wdrWawukB/V39EzQfWEDL3OsLzvouKq/t4P4ahjxonNB3W3LGVVMrGcifRcRC09+IUfUS1qzGEm0S+G4mNQE3tVaa3GdlhSkpJW+xbICVuvQqXUYZLqyRhHqU/vWWyw1NmsHnLahBCkM9bI9uyGRPd0KifP36VlSEcYy+UBjOySi3odXPf+sX0DSXpHUoykEjRMTjE8vpKleRRlHFEM2lAnNGHx2M4aBuKnX1HmQLEmaWVwgH2OfY7T/6Q94xDewJRaua3oWnVOI0S8kjyIohDRnHRRd7OYGgenJrqw6UoilIo/ekU2liLmGga7fHxxomx6AUZJwJFPmzLHrUtVNpJcWUPul6DQ4tgAXmCuOjCwSA5O0HAUaV6tylXhBlZyWPag2Ssk7i009ljIQQOLcRgZgcwa/KCU2a0itpiNj1wFb95fCfvFO7ousaDv38jvnEaSQOUe5ZxZOg5LDs3MiUha8Vx6D4irpm5Ut2mZXOpK42w43Ab6VyeVY1VLK+vmlBjQEWZiYo9XjTAtC0c2umb3pRpMjscOfuOegUI1/AULXH6uhXPDvBi2wIOJl5mbVUt19bOwmVM/DZkzoo6/GEvgz0xwqVBAGy7Hd1wECoOYuMile8jLzPDncmsTtJSY0nkYbRLtDKhoijKTFTu82OfarisvSvRY1o29cFzjRN1IACZh1PXZWnbxDJxnjpu0pl9hWtrZrG2unbCDf8BZq+o4fCrJxgaSBCI+IYXD7Dacfuc+ENeHHYtPen9SJFDlxLb6sSUJSyLPDrhcynKVDQj73Y04Rie/8Lw6kXvkNhowoV9th2VS05KOXxjLhzoM/RmfMNdK1i0qp5jTSfRNI15y2oJF5/f02e/o5ylkYfYH30caQ1XAzl0H6uLP4I+Ayt53jG3soS5lVNjSp6iTBdeh5P3zZ7P44f3U+T24NINBjIpPIbBTXVnn3IlhBPp/RAkvwHoIJx0J7rZ2+/m+Y4ybDHEgb432dHRzl+tv3ZkKuX5croc3PUH17Pv+VaO728HAUuunUXtvFaEEBjCQ7l7KUNmO3mrA4dWxarwRymfYdNVFUVRLrUyr59rq+t4+UQLxW4vDk2jL5OiyONlXdXZV6oVWgjpvh/SPwWcIHROxjrZ1VfMaz1BJIPs7e5mT083n1i1ZsI9crxBN7/7Px/giX/7DV3HexFCMHflHKoa+gGBSwtQ7llCLNeOtNO4jTrmh3+bItfFTSdWlKliRn6LNrQAQddS4rn9uPThpaWltLDsIYo9j9A9yfHNVAPZ47w9+HOGzC50YVDvW8+C0K0zsklmaVWY0qowwJhPSM6l2reGUs9iotkWNOEg4mqY0Qke5dL54he/yI4dOzBNk49//OPccccdIz+79957CQRON+b9whe+QHl5+WSEqVyEe+csIuLy8HTLYaLZDKvKq7lv7iJKPOdu4q651iP1cmR2C5lcLz9orqA/v4yAe7iyJ+h0cbCvl7d7ulhdWT3huEKlfj726QdJxIZL/n1BD0OxXsz8MXStHEO4CRthhLOScPgzaBc5TaszFeO13maiuTRLw1UsL67FqamSfkUZjxonrny/u2Q11f4gm1uPksyb3FBTz71zF+FznPv+XbhvB6MemX2VaHqA77fUMmQvI+Qe/noadLnZcfIEtzbMZnZR8YTjqp5dzh/946PEB5MYDgOPXxAdbMWye9BECQ7hpcgRRtfnEwr/3UUv33480c/rvcdJWTlWFtWyJFKFLlTVuDI5ZmSSB6A2+Ns0R/8PabN9eOEPJCXeW4i419LNockOb8ZJmL281vsNNGHgN0qxsTiW2EJOpllZ9IHJDm9SJMwsPz26j1c6WrClZG15LQ/PXUaR2zvuvk7NO+OaLCuX186dO2lqauJHP/oR0WiU97///aNu3gG+853vTFJ0SqEIIbhxViM3zmqc+L5GA8Jo4HC8k32x16jwn566NTxFWqOpt/eCkjzv8IdOXw8Dwb8kmfw2uewOwMZwLMLve+yiEzxv9Z/g3w69gkTi0HS29RxjfrCcP1t0E059xt5GKcq41DgxMxiaxp2N87mzcf6E9hNCgGMhwrGQvf0tNA29SXXg9DVVEwIp4XgsekFJnnfOESw6PQYEQ39LMvGfmOYeAJzO1Xh9v33RCZ6Xug7z/WM70YRAF4Kt3UdZU1LPx+ddd94PaRWlkGbs3YlDDzOv6L+TMlvI2zHcRg0uQzVinSzHE9uxpY3XGO6voGPgN8poT77JwtBtuPXgJEd4edlS8sXdW2mODVDq9SGA17tP0DI0yGfW34JLfbFQJtnKlSv58pe/DEAwGMQ0TWzbRjs1dz6ZTE5meMoUEnA6x2wIb0lJkcdTsPNoWpBA4I+R/o8hpY2mjZ8QH49pW/zXsR0EHC68xvBTaSklh2Ld7Oxr5dpyVdqvKGejxgnlfPmdTrQxciEa4He6CnYeXS8lGPoUtj1cBVqIcSJhZvlRyy6KXd6RxL+Ukjf6WrmufA6Lw+MvnKIohTaja8iE0PA5ZxNyr1IJnkkWN7sxtNEXcSE0BIKMNTRJUU2eI9E+mmP9I0sX65pGhS9ATyrO3v6uyQ5PUTAMA59veMrOT37yEzZs2DBy4w4QjUb55Cc/yQc/+EG+9KUvIeXZ1n1TrnQNkSJqg0G6k4mRz0E8m8Wha6ytPnvPhrGYlsXuEx1sOd7BjpYTZMz8Ga8Rwl2QG3cYnqaVtnIjCZ7h4wt8Didv9rcV5ByKcqVS44RyvpaUlhNyuelPp5BSIqVkIJ0i4HKxrGxiU/gyZp593f08+XYTu090YFrWGa/RNG/BxomWRB9SylGVncP94TT2D3YU5ByKMlGqHECZEopdjfRmj+LWT8/NtmQegYbPuLASzemsL5MEzlySUgroTiUmJyhFGcNvfvMbfvzjH/Otb31r1PZPfvKT3Hnnnfh8Pv7kT/6EZ599lttvv/2M/Zuami7ovJlM5oL3vdymS6yXMs47I6U8PhTnaHcXAgg6ndxf10Bvayu953mMtJnnO3sO051MYds2L7V2EHI5+Z0V8wm7z/9Jr5W3sW0bh3P8W6ABM008HseRzo+6HkfzGRKmc9zf13T528P0iXW6xAnTK9ZLSY0T5zZd4oRLG+u9pZX8tPUYR2PDS6iXud3cVz+b40ePnvcxopks337rEIOpDJreAkC5z8NvLZ+P13H+X3vz5nBiyHCM33vtZDZGPBHHmR2dTBoyUwx299KUuTLGiekSJ0yfWC9lnCrJo0wJs/xraEm+RsLswa2HsWSOrJVgYeh2HFrhyvmni3KPHymGn2RkSDBod5CTGXKajsOxcLLDu+QGYikGzUJ3AAAgAElEQVR2H2wnlkgzr66MBQ3lGPqMLjyckl555RW++tWv8s1vfpNgcPSUykcfPb0M6Q033MDhw4fHvHlfuPDCPs9NTU0XvO/lNl1ivdRxrl++nL5UCtO2KPf5J9yn4Ce79pJAMKeqkmh0kHA4Qk88wZuxDH+0csW4+2fSOTb/dCe7thzCylvUza/k7t+6hvKaorPuI6XkVdFHc6KPMpcfIQQ52yKdETyw9FrmBc9dBTxd/vYwfWKdLnHCxcW6a9euAkczOdQ4Mb7pEidc2lgXAhtWrqQ3lURKKPP5Jryq1r++vB3pdFGma4TDw0u4d8aGaDbhA8vGjzsxlObp77/G3p0tSFsyf8Us3vfo1URKA2fdZ65t8/LuLpJmlohruDooY5kEcjr3LL+GCs+5W05Ml7//dIkTpk+sFxvnucYJ9a1JmRLceoDry/6QOt86JDYePczq4keZG9w42aFNitmhYhYXldOaOkl7vomUHSedN3E4cmwd2EZ76spdA+5Iay+f++ZzPLllH9t2N/ONx7fx9ce3YebPLLdVJk88Hufzn/88X/va14hEIqN+Fo1G+ehHP4ppmsBw8825c+dORpjKFFPi9VLpD1xQI8rtLSco8o0ury/x+9jT3jlmOf57/fTfX2TH8wcIFvkoqQzT0dLLNz73JEODZ+8LIoTg4/Ouo9YboTsTpycTJ5ZL80jjmnETPIoy06lxQpkoIQRlPj/lfv+EEzx5y2b3iU5K/KNXfyzyednefGLc/W3b5tv/9DR7X28mUhqguCLEkb3t/Mc//ppc1jzrfoam8ccLbyTodNOVjtOTjpPKm3xs3rXjJngU5VJRlTzKlOE1Iiwruo9l3DfZoUw6IQR/svRq/mZPEydSOkIa1Pr91AciJK0Uv+neyWMNd012mAVn2Tbf/fVO3E4HPs/pJqcHm7t588AJ1i2rn9wAlRFPPfUUsViMT37ykyPb1q1bx/z587nlllu4/vrreeSRR3A4HCxevHjMp7OKMhGGpmG/p2eHLSWaEAjO/WWgtyPKobdPUFoVHvniEC4J0NsZZc/2o1x/x/Kz7htxefmbZbdzIjlIyspR643gcxSuEaiiXKnUOKFcbpoQY44TujZ+XcPxQ110nhigtDI8sq24PEhvxyCH95xgydqzrzJZ7Q3zv1a+n9ZEPznbot5frBZJUSaV+vQpyhTl0HV8Lsn1gdmjnmYEhJe21JXZfLm7P04ilaU0cnq5SyEEXo+Dtw6dVEmeKeThhx/m4YcfPuvPH3vsMR577LHLF5Byxbthbj0/232AqtDp1Ut64wnW19eij7Usy7vEBpNo2pl9zhwOnd6T0XHPLYRglv/s07oURTmTGieUy8nQNdY31PLqsTbcpxI9UkoGEinuWbYQKeU5q4Ni/QnGXAoSGOyNj3t+TQgaAiUXFLuiFJpK8ihXnN7uGD0dUYJhLzX1JRMu95wqdKERdPjI2iZu/fTKLmkrS4krfI49py+HoWOfWlXh3X83y5K4zqNJqqIoV65bFs6huW+Qt9u7SCQzdMe6yXelOPzKIF9+ppVbH7iKxavqx9y3pDyIbctRyzcDmLk8NXPUtCtFUZQrwYOrltARi7Ov9QQZbYjBvgR6d4bXtr5G+6wj3PHQWhrmj72keWnV8JTCd9+DvrPiW1lNZMx9FGWquuCePP/8z//MI488wv3338/evXsLGZOiXBDLsnniu9v450//gh9+cwtf+8LT/Pv/fprEUPqSnC9uptmX7uSVnoN0pgcLfnwhBDeWXkXMjJO1csBwgieZT7OxdHXBzzcVlIR91FVGGBhKjWzLWzYZM896VcWjKDOa0zD44xvX87d33sgaV5Cy/SnW5IJUVUTIZky+/9UXOPT22H0XwiUB1m5cSM/JKKlEhlzWpLcjSqQ0yLJ3leBnrTymrfp/KYqiTEd+t4v/dtsGfmfFfFbrEaoOZlgtQ1RURhjsT/CtLz3LyeN9Y+5b3VDCvOW19JwcJJPKkU3n6Dk5SE1jGXMWV4+8LmPlydv25XpLinJBLujR+Pbt29m7dy8//OEPOXz4MJ/+9Kf53ve+V+jYFGVC3nztKDu3Hqa0IoymCaSUnGzt59c/2cnDH72hoOdqip3k60dfZHAois9qQwC3Vi7jruqVBa0cWlO0EFtavNDzBkPZJAGHlwdrb2ZhqKFg55hKhBB8+O61fP2n2+geiKMJgZTwvusXMb9ePW1XlJlOCEFdUZjBnT3UBIJ4vMO9cbx+N7YteeFXbzF/We2Y+9756NWUV0d4bfN+Mukc629ZzA13LsftddGdivO9Q2+xp68LXRNcU1HHw3OXEXCq3juKoijTiaYJqrxeXn/tEHVFERynKsEDIS95M87W5/bx8O/deMZ+Qgge/oObeW3zPna9fBDLstl4zyquu30puqFzfGiQ7x7azdFYHw5NZ2P1bO6fswS36r2jTEEX9KncsWMHN998MwDz5s2jp6eHdDqNxzPzlrpWpo7XtxzCH/SgnerNIISgqNTPvt2t3JPO4fY4xznC+claJv9x7GU8ugPN8BHxhLGkzbOdb7M4VENjoHDJCCEE60uWsqZ4MVkrh1t3ookre1G84pCPv/7dTbR2DpBM56gtDxMKqGuLoijDbMsmHs1QUlo8arvH66K38+z9dXRdY+1Ni1h706JR21Nmjs/teol4LkeFz4+Ukq0dLXSm4vz3qzZeVOJeSkl75yCdPTH8Phdz68swDP2Cj6coiqKML53MYZrWSILnHR6vi+72gbPu53QZbLhrBRvuWjFqe186yed2vQRIKrwB8tLmmbZDRLNp/nDZ1RcVq5SS5rY++gYSRMJeZs8qHfkuoygX6oKSPL29vSxYsGDk30VFRfT19VFbO/bTM0W5HHI5a1SvBRhOkkhbYttjd1JLZ012HT7BgeM9FAU9XL24nuqS0DnPczzZS87OE3Z6yTI8rUgXGobQ2BNtLWiS5x260PAa7oIfd6rSNEFDdfH4L1QUZcbRdI1IqY9UIosvcPq6mIinqaqb+HXjzd4OBrNpqnynlroVgjKvl6ahFp7rCHNt+QL8hvfcBxlD3rJ55pVjnOw9AKfW/yoKe/n9D91AccQ33u6KoijKBfL6XbjcDnJZE6fLMbI9mUgzd0n1OfYc29aO42TzeSr9AQAcQqfM62Vr7wFW9IZZVdSIW5945Wcma/Kz5w4RTQyPExJJTUWEj3/wOvw+VUmqXLgLSvI4HI5R/z5bt/KmpqYLi2qSZTKZaRv7pTIdfiel1S52bumgqPT0zXM8lqGk3E9rW/MZr8+YeX6w5RA9sRQuh45lSZ7atpd71zYyt+rsDdZac4Mk4nEcaQvLshgcHO7HE8+n6bQ7aUpM7d/TpTYdPiuXm/qdKErhCCFYd/Mctj55DNu28fhcJOMZctk8m+5ZRTqdo68vTjDoIRQaPznTlRqeGvqOtIzTZR8href4dVecbYNvcE/1DayKLDjHUc606+1WDh7rY3ZD1cg9Uv9gkp/8ehef+K3CTiFWFEVRTtMNjZvvWcWvvrsNf8iLy+0gHkuh6zrX3bqERCLD4GCSSMSH3z/+Q9T2ZAzXu6owE/YAPXYLWd3kpyc283yPl4drb2VecNaE4nzxtcO0dcaYXV85Mk60dw7y1Iv7eOiuK7P/pnJ5XFCSp7S0lP7+/pF/DwwMUFJy5pJxCxcuvPDIJlFTU9O0jf1SmQ6/k/q6Rob6f0NHWx+apiGlpKgozGN/dCsV1WcmbZ5/8wipvMbcWVUj21LZHNubo9x543oMfexpUbOtPC/uaUXXNHLxFJFIhLxtkckK7lh4NQ3+0gnHbuUtUskcXp8TfZqX8k+Hz8rl9t7fya5duyYxGkWZ/urmlTL7zxt4dfMWuk4OUF03i5vuXkFL+wDf+K9XkHL4AdSKlXXce+9qnOdYna8+GME+tYKKLS26rCMgBZp0UeEpxqkJft7+ErXeCkonsLLhjreO4/U4Rz0EKwp7OXq8l6FEhuB5fLFQFEVRLsy6Gxfg8+tsf2kb/T0p5iyuZ8Ody3ltZzPbXzs6XO2P5Jpr5nLHHcvRz3LfDzAnVMIbPe0A5GWWHrsZTRpoUqPKW4wlLX5w4ln+av6H8U2g8n7H7haCPteocaKkyM8bb7fy4J2r1LQt5YJdUJLnhhtu4Etf+hKPPvoo+/fvp7a2Frdb3awo5yal5Gi8j67UEBGXlwWhcgytcP1lPF4XH//L2zi87yRtLb0UlQRYsqoO31lupN8+1onfM7oU0uty0hNN0BdLUlEUGHM/p27wsTkb+fcjz9OfT5FNC0DwvuoV1PvOTHaei5SS7S8f5IVfvUXmVN+gm+5ewfoNC6bt0u+KoiiXnNaMv+w3bPpQHyBxOZbT2VbD00/vpaQ0gGHo2LZk1xstuN0O3v/+VWc91LLiSmb5w7TFo3hcOUzy2JZBmceH33AwXEIPB4eOU1q64qzHeS/blox1FRfi9LK8iqIoyqWRzu6kuPE/uaM+DoDHdQ373ipi69bDlJYG0HUNy7LZ8vJBwmEv1103/6zHurayjufaDtOZiONwJTClhbQ0ZgXCODUDMEjkUzQn2lkannPeMQ7PhnnPRsHIgwrGHEUUZXwXlORZsmQJCxYs4L777kPXdT772c8WOi7lCpO18vzfA6+wP9oFDF+yKr0h/mLJjURcE+91cDaGoTN/eTmLVtQixmlQHPS5aO8Z3aTTlhIpJe5zPPUFmBus4NPLH+TZva9RWVPNnEA5pe7ghON9c9sRfvX97YRL/PiDHrJZk199fzsut4NV689/kFAURZkp8lYPwvEtbFmCoVcipU3WfJuu/ib8gbtGGhtrmqC4xM/rO45xxx3LcTjGrpJ06jp/vWoDT7ce4jede9AQNISKqfEHefcNdl5ObGn1q5bN4sDhtlFT2qNDaWqrilQVj6IoyqUkTjAw9G00LXRqnLBIZbbS07+XSOT2kaodXdcIR3y8suXQOZM8AaeLv11zE08eb+Kl7rcwNI3ZwVIqfKMfCE90nFi9tI5fP7+b0ndNAhiIplixuPqclUWKMp4LXvPtU5/6VCHjUK5wm08eYu9gJ1Xe4MjNbldqiB817+YTC68tyDl60ns5EvsVaasfQ/PQ4L+FWf4bzloRc/3SRnYfOUnOtHA6dKSU9A4mWNJYQdg//mpOPsPFQnc5C0vnXnDMLz39NsGwF9eppnAul4Ng2MtLv94zbpInkc6STOcoDnrVai2KoswYycxWII+uDSfWhdDQtQpcnj2EIoNY5unr9ztPak0zf9YkDwzfwD80dxnva5jL/z74HfyGF43hG2xL2gDM9U9scYl1KxrYun0fPf1xpARNCAJ+Nw/fvVpVaiqKolxK+msgDDRtuE+nEDqGXkGk5C283o1Y1un+sg6HTjSaGveQxW4vv7NgNXfUN/AvR35MxOE71VIfTDuPQNDgm1hT503XLeCNtw7T3TcEcrjnXGmxn7tuXjah4yjKe11wkkdRJuKV7mNEXJ7Rc049Pt7oayNrrcOlX9xHcSB7lD0D38Kp+fHqpVgyx6HYE4CkLnDjmPvMqy3l4Y0reGLrPqykjW1LFtSV8eims5f1F9pgf5ListEVQC6Pk4HeobPukzXzPP7SHnYcaEMIcDsM7tuwjHWL6i51uIqiKJPOsvpBjB4zhBD4fR5y2UF07XSftUQiQ3lFCI/HeV7H9hke7qnewBMnXxo1peqG0hVUeybWb83h0Ln7pnm4fKWc7I4S9LtZOKcCt8sx/s6KoijKhdMGEWJ0xaQQOj6fm1R6AJfTP7I9Fk2xYH7leR+6zF3EzeVreL57J++eUHV31fWE33Xc8+H1OHnojoXo7iJ6+uIUhX0smF1xzocSinI+VJJHuSykZCTb/Y73/vtitMQ3YwgXzlMZe0O48FJES3wztf7r0MTYH/XrlzVy1fxaugbi+D1OSsMTuzhfrFmNpXR3RAmGT09Zi8dS1M0++zLsP9+yl9f2tVIa8aFrGpmcyXeffYNIwMu82ok3fVYURZlOXI5FwK9GTYOSMk9xsQ9BNT09Q3g8DnLZPEJo3HvPxCpnVkbmM8tbwcH4cUw7z9xALVXu0guqvtE0wZz6UubUq2uzoijKZWPNw7a3jlR8AtgyQ1lZCWY2xFB0CLfHQSZt4vY4ufW2pRM6/I1lq1kQqOdQvBUNwYJgPaXus6/Mey66rrFwTiUL55x/oklRxqOSPDOUlbc4uv8kbYc6CYS9LF7bSCDsG3/HC3RdeSNPtL5NlX56ulZfOsGK4pqLruIBSOV7cIjRvX10zUUmH8WSWQQ6J+Ix+jIpKrx+qvynL/oel4OGyqKLjuFC3Hrfav7jS88y2BfH63eTSmSwbcmt9429bGI6a/LavuMjCR4At9OBy2ny0u6jKsmjKMoVz+O+CmnXkrfa0bQQyDy2TBAJPcQnPnEnO3c209LSS1lZkHXrZlNaOvF+acWuENe6ll+C6BVFUZRLzlqDoR/GzLejayFsmUXKDBXFn+BP/nQ1O3Yco6NjkNqaItasnU04PPH+oBWeYio8xZcgeEW5eCrJMwOZuTzf+/KzHDncglacRpqC5x4P8dhf3c2suRWX5Jy3VM/nQLSLI0O92FKiCUGp288HGwszNSrkrKcvvR+Pdvpia9ppXHoY0zL45z2vsrevC00IbClZV1HDx5etwaFNbjlk/Zxyfv+v72TLs/voaOtn/rJaNty2lKpZYw8aqUwOCSMJnne4HAYDQ+PPJ1YURZnuNOGC3McI+7tIZbejCR9+zybczpUIIdi4cREbN16eWLoG4mx56yht3VFmlYfZsGIO5WdZmVFRFEW5XPyURT5NIv08mdxunFoxfs+tuJ2L8Hng9tsvX8+btu5BXn7rGN0DcebVlnL98kYigcItOqMoY1FJnhloz7YjHI7vwnV/9/AGAfm4wY++K/jL//kRtAIua/4Oj+Hgr5fdTFO0m85UjCKXl8WRyoJU8QA0BDbRm9lPOj+AUw+Qt9OYMsXSyG/zs6NNvN3XSZUvgBACKSXbOtqoDYa5u3FBQc5/MarrSvjg7914Xq8NBzz4PS7SWRPPu/o6xFNZ1i+uvzQBKoqiTDluAt47CHjvmLQITnQP8uWfbMGybLxuJ+09UV4/0MafP7SBmrLwhI8npeRYdIDXO9uxbclVldXMLypRTZoVRVEugK6FCPnuJ+S7f9JiaDrexb/94jV0TcPtNHh+12G272/lLx+5keLQxGdQSCnZ39fD7u4OnLrO2spaGsIXNk1MubKptdlmoF173kRfexIt60RPe9BTHgyvTXTeHvq6ouMf4AJpQrA4UsGm6vmsKqktWIIHIOCoZk3Jn1Lsno8ls/gcFaws/j3KPCt46UQLZR7fyI2yEIISr5fn244V7PyXi65pfGDjcoaSGfpjSRLpLN0DccJ+D9cvb5zs8BRFUWaMX766HyGgNOLH53FSGvEjgV++uu/Cjne0ic+8+iK/aTnGC23N/H+vvcyPmvaOagCtKIqiTA9SSn7y4h68bgfFIS8+j5OySIBkOsvzuw5f0PH+c++b/OOOV3ixrYVnmo/y6a0v8FzL0UsQvTLdqUqeGShb1g02CPv0VCWRdYF3iLjoo4zJ6U9zvrJmnjdaTnKgs5tiv4+VDQF67W10pg/g0Dw0+m9mbvA6dGFg2TZ52zpjepMuNJKmOUnv4OKsmFvNXzx8Iy+/dYzeaILrljVy3dIGQuex7LuiKIpSGIdO9JzRrD/s93CorXfCx+pJJnjicBNlPj/GqfHKsm2ebj7MtTWzqA1OvDJIURRFmTyJdJa+WJKyyOhxIuh3c+B494SPd2SwnxfbWqj0B9BOPbg2LYsfNr3NuqoaQi73OEdQZhKV5JmBauYX0d0ih1e8OlUFnsuYuEtdeEPnXtrVknkA9LOsVnWppXImX3zmFdr6o7gcBjZp9qZfprHMT7m/HFvm2R97hmS+n9XFD6BrGivLqni7t4sy3+myyL50io2107fypb6yiPpJahatKIqiQNjnIZvLj5o6mzXzhPwTu9HO2zGO9n+d22e9hEt30pVeysnkVaC5kBIO9vepJI+iKMo043IYGLqGZdsY+ukH69lcnprSiV3Tc/luWge+yl31O9E1H52pFXQkV+HQdaSUHBno56rK6kK/BWUaU9O1ZqCr5l9NuMJPJp0lk8qRTuVw+DRq6ioocVeNuU9Opnit7yc8fuIz/PTE/+LV3h+Syscuc+Sw9XALbf1RKsNBinxeKsr6cRgmbT0WAh1DcxE0ymhLvkkyPwjAI/OX4XM66UjE6UklORkfoszr457ZCy97/IqiKMqVYdNV8xiMpzHzFgBm3mIwnuaWq+ad9zFsmeXE4OcweINc3oNlO6nx7WR+6ClAIgS4DPU8TlEUZbpxOgxuWDGb3mgSy7aB4QcBqYzJTavnnvdx8naME9HP4tEPkjb9SKlR73+VxuBLp8+lT+5CMsrUo+4cZqAa7xzWzL2Gw8VvY6YtNEPg8bnZUHYfDs11xuttaXGAp9CTJj6jCIHgZLqJmPn/s3ff8XFd54H3f+feO71hZtBBFPbeRYpNheqSbcmS5Uiy49jeJI7tJN58dt/YXifxu97PepN8kn13nc3aiZ2sLTte926rWI2UKFaxF4AkWFCI3mYwfe695/1jKEAQGwiAKOT5/iUNZu49lyDn3Puc5zxPBw9W/DG6uHr2z0Q62NSO3z08Rs05gC6cpEyLTD6Px+lACA0hNJJmHz4jTJnPz3/b/AD7OlppTcSoC4W5rawKjzF5434nKSXNqR7i+SRl7iJK3TfXCq2Ukq70IDaSMndgxhQNzVsWJ5o66epPUBr2s6SmDIehJk1FUS5vy4o5JNM5Xtp/EtuW6JrG+zYtYfPy0WeJJrKHyFkdRLy1iP4WMrbANiMUuZrRaMWpR1hZemO6XiqKoig31ns3LiFvWuw8eg5JIfDzzH2rWTp79N/r8cybWHacqK+GxlgLOVvHlmHKPMc50beCgDPEwmjxjbsIZUZSQZ5bkCZ07ix5gvn+1bSmG3FpHup8SyhyXv4LoitzjhT9VDpmD70WMIqJ57tpTzcyyzt5GTF+t5PWfmvo/+18CLxNSBxDdXektJHSxqsPB0/8Tidba6Z+e1Yin+Zfz75Mc7IbgUBisz66gA9Ub8KY4nbuE+FCaoBvdB4gOXAQgaDcE+D352+mxj+9t5YNpjL8w8930N47OPRaRSTAn75/C0Gf2uOsKMqlNE3w8MbFbF0zj1gyQ9DrIhXPEO9PUhT1X/sAQM5qQwCGprGipIxj3V2kTBMNG5c2wGfWvkfVWVAURZmhDEPng1tX8cjGJSRSWYJeF4mBNIl4mkBodG3UM/kmhHDh0Q2WFpdR39tFzpaARdCR5KMrHpnQZjbKzUH9jbhFaUKjyjuXKu/ca743ZcWAS7t7SGxS5o3rxnU5dy2czcGmdvJuC4euYyZrsN3HiQRNDF1g2jmSZh+1vjX4HdFJHdto/OLCHpqT3ZS6ggghsKVkV89JanwlbCye+nbu45G1TP7n8VfpMzPUhkoBGMil+J8nXuW/rnkUr+Gc4hFe2a9319PeO0h5JDD0WnvfIL/ZU88z96yewpEpijKVkmaWvG0ScnivmJXodjnobhvgn//hZXo740igdm4pT37sjmse36lXDs2uIbebjVXVDGQzIDXun/deQm6VxaMoijKdJfIZLGkTdHiuOE/43E4unOniW9/ZSSKeQUrJohWzePx3N1/z+G6jhkR2DwAlXi8Rdw0DmTRCaLxv4fvxOFQLdeVSKsijXFPAKAYEUsqhL69CS1dB0FEyqWNZWlXGB9ct4xcH65FSYkvJAt97WDOvh978aRyaiyVF97EgeNekjms0slaeg/3nKHYNb2HShCDk8LCju37GB3lODLQTy6UJGa6h6ytyemlPxTnW38b6krqpHeBV7DvZTHHIN+K14pCPvSebVZBHUW5BSTPLj5t3c6jvPBJJiTvE07WbmBsou+S9iXiab33ltwhNI1oWBOBCUw/P/uNL3P/Bq9fn8btW4tTLyJodOPViEBKfow+vYzlB1+hr+yiKoiiTqz+X4Afnd9IQbwOgxlfM07WbqfReGnTpah/g3776Kh6fi+KyILYtOXmkhR/+n+3cfn/1Vc8T9GyhP/U8OasLhxZFCBO/o5+Q5x48jtIbcm3KzKeCPMo1FbtqCFFJ3OzCq4cAQcoaoNhVQ6l79jU/P5GEEDy4fAFbFtRxoT+O3+2kIlQImrwzCHUjdKT7aEp14tIcLAjMwmtcXwq9JW2klGiMHKMmNPK2OZFDnRJJM3vZ1yWSRD4zyaO5PpqmXQxcDpNSDm0BVBTl1iGl5Ntnt9EQb6fUFUAgGMyn+drp3/L5JY9R7A6OeP/xQ01ksyYl5aGh18LFAXo6Y3S0xFi69Mrn0oSb6qLP0538EYOZPQhhEPY8RNT3+IypZ6YoinKrsaTN1069RE82TqmrMCd0pPv536de4AvLnsBnjKxxun9nI1JKvL7C65omiJaFONPQwaK1V995YGghqsN/QXfiRyRzB9GEl2LfBwj73nNjLk65Kaggj3JNQggW8QAi1MfZ5FtIKVkaupuFwS1o4vrqyExUIMbncrKgfGQNoRt1Qyyl5Ln23ezoPoqNRCBwa04+Nueh6zqO13Ax219Ga6qHiHO4XkMsl+LBipmfLVLrjyJFIbvqbfbF33etf/ptnXunjUvqePXQacrDwwHDnniSe1bNm+qhKYoyyboyMU7G2ym7uK0WIOjw0JWJs7e3kUeq1ox4f7w/xWWnHwnpVP6a5zP0MBXBT1Ae+EPgxs1liqIoysQ4M9hJVyZGmfsdwX2nn45MjGMDzdxePLJ71kBvAodz5GO3EAJdF6OaJ5xGBVVFn7nhC9rKzUMFeZRR0YWDxUV3s7To7jF9vrutn5d/uJf6A+dwe11semgFW96zCsMx/YsNNyL3PFsAACAASURBVCYu8HrXEYrdIXRRyOxImmm+e/5lHhPXF5x5snoTXz39HJ2ZGLoQmNJmljfKHaVXWeqdIWZ5i9hSOo8XzhxCy7oQApJmjg3Fs5kTmN5V/x9Zv4iWrn7OtPciJQgB8yuLeWT95BUVVxRleoibaTShXXIj7dA0erKDl7y/dl4p9vNyxM23ZdlIJMXloyvADFcP7tjSpjnVQUe6h4DDyzx/DS59+tY5UxRFuZkN5tOXfV0A/bnkJa/PX1LJsQPnR7yWz1sIIYiU+C55/5VcbZ6wpMXZxAV6sv2EnUHm+WtuiqYuytioII9yww0OpPiX//oLsqkckdIgZt7ipR/uob87zuN/uHWqh3dNRwfO4tD0oQAPgM/w0JOJ0a3FrutY5Z4wn1vyAQ73n6MnO0iNt5glRTU4tZn/T1EIwUfm3o5/IMcFr4WNZFPJbNZEa6f9qoPH5eDfP3EHZ9t76YklKQ75mFMRnfbjVhRl4pW7i5BITNsacYOcsU3mBy4thDx3USXzFldy+sQFfH43ti1Jp7JsvncJofDouqdcTd42+UHzi5xONCFloZab3/DysdmPUuxSBTcVRVEm29t1d2wp0d5Rr1RSqM3zbsvW1rH7tQbaW/vwBdzk8ya5TJ5HPrgel3v8pQFSZobvNP2K9nQ3tgRNQNQZ5mOzHyXgGH0QSbl5zPwnS2XaO/hGA6l4mpKqwheiU9coqSriwOsn2fr4bRQVB65xhJuLz3CzqeTmzBDRhGCJr4QPLJ4+12dJi95sB0IIos5yNHH5yVQIwdzKYuZWTu+sI0VRbqyAw8MDFSt47sJB/IYLQ+jEzTQV7jCrI5fWodN1jQ9/6h4O7znDob1ncToNbtuygCWramhoaBj3eA7013Nq8DwlrshQ4HkgF+fnLa+x4EQNu547RGoww6K1s7n/mU0UV6jAj6Ioyo1U4QlzW3Que3pOEzDcaEIQy6dZEKxgQaDikve7PU7+4D8+xP6dpzl+sAlfwM36Oxcyb3HlhMwTb3Tvpy3dTYkrMvRaT7afF1rfpGiPn70vHcXMW6zcvJB7Png7wcjos0yVmUkFeZQbrr2pF6fbMeI1TdPQdUF/V3zaB3mWF81hT289lrRHbNfyGR5KROgan1amUkemhVc6f0baSiEAr+HnvrInKHFVTvXQFEWZxh6qWEWFO8wb3fUkzSybSxexpXQR7itskXI6DdbdsZB1dyyc8LEc6m/Ab4xs4R5yBDhw+gSnfnCW4mCYUHGAhrfOce7EBf707z5MIKxWbhVFUW6kZ+o2My9Qxs7uU5jS4r7yFWwsWXDFLVJur5PN9y1l830TX6Lh4MBJihwjmwKEnUFeOrKL6I+DREpDuL0u9r92nHMnWvnjv/3QJc9mys1FBXmUG65ydgnH9jSOeM22bSxbEi4NXuFT08c8fxV3lq7gje6jQKF1vFtz8pE595Fu7p/q4SlXkLFSvNDxQ3R0ihyFlY20leT59u/zdM0f49Rc1ziCoii3KiEEqyJ1rIrUTcn5pZRkcyZOh1EoBv+un+ezeQZ6BqmtqMBlFwJPkfIQ3W397N92grsfXzf5g1YURbmF6EJjQ/ECNhQvmJLz27YklzdxOQ00BPJdM0VqMEMilmJxdd1QFntxZZjuC33Uv3WGlVsWTcWwlUmigjzKDbdq8wLe/M0h+jpjhIoDmHmT/u5B1m1dMu2zeKBws/+eyo2sDS8caqG+MFCNx3BRjwryTFctqTPk7Rx+x3BnL4/uYyDfS2vqLHP802dLmaIoNw/Ttmgc7CRpZsmaqev+/MGGVn65/Rj9gykCXhfz14VJuDvw6u6hbJ7uZD/ePjdue2RmkcvtoO1s14Rch6IoinJj5CyT04MdZO08ppW5rs9KKdlx8Cwv7mogkc4SDXqpWl/Oef3siG29Pal+Aq3eS8oUaLpGZ3PvhF2LMj2pII9ywwWKvPzhFx/npR/toWH/Odw+Fw8+vZEtj6yc6qFdl3JPhHJP5NpvVKaFnJ2FS9a/QSLJ29nJH5CiKDe97kycr556id5cAiQMJhK0NZl8oGb9qAq5H2ts51u/3EMw4KYsGiCTzbP3tT7q7i6mR/SBLCw8hL1B5GGLTMgCTeCSAoEgm8lTWVcyCVeqKIqijEVzsoevnX6FZL4Q3EkkEsTaDe6vWD6qz7956Cw/evkQ4ZCHsmiAZDrHgVeS1N1TRK/ov7jpQFDpLaGnXiNTYoEQuGUh2GNbNqXV0aufRJnxVJBHmRTR8hBP/+kDU3b+eN8g8d4E0YoiPH7PlI1DmTxl7lmAwJb20CqGLW0E4uLPlPH6yle+wq5du8jlcnzpS19i+fLhG5SDBw/yt3/7t2SzWe6//34+/elPT+FIFWX80ukch4+00NLSS2lpkNWragkGh+cTKSXfPvsGsXyKMnehXpuRtnit6wTzg+WsDNde8xy/3d2Az+vE6y5k6LhdDiJBH7H9kk9+dCud2T78hoeoVsIXl/+CnR2dGE6DkNSYfcEm6nOxZuuSG/MHoChjoOYJ5VaSSGQ4eKiJjo4Ys2ZFWLmiGq93uDyAaVt8o/E1bGlT5inME1ra5Jet+5kXKGe2/+pBetuWvLirgXDQg9tZqKnj8zixLBujvpSPP7aV3lyMIkcAtxXg8wt/zJuD/ThcBhFLp7bZpLwkyKK1lzYRUG4uKsgzRZKpLOlMnqKQF0Mff+s85fLyuTy//OqLHHjpCELTEBrc/dRm7nlmi2qPfZOLOstYElzD8dhbOIQDCZgyz8qijRQ5VQet8dq9ezdHjx7l+9//PqdOneJLX/oS3/3ud4d+/vnPf55vfetblJWV8dRTT/He976XmpqaKRyxcrOzpWRfWyuvN5/HkpLNs2rZOKsaQxv/HBuLp/nnr79Kb18Cp8MgnzfZtr2eP/rDrZSXFwHQm0twPtk9FOCBQsdBr+5kV/fpUQV5uvoG8XlH1gtzOw06exOUOYup8pYhpeS/vbydbLmbec4yOpt7GJA5Guf7+PRT71VdU5RpQ80TynSTsyx2tTazs7UZp65zV+1s1pZXTsgzQVdXnH/6+qukUjkcDp23Dpxn2/YGPvVH91BU5AWgOdlLLJcaCvAAGEIDobG/9+w1gzx502IwlaX0Xd/zHreDrr4Etb5Kan2V5EyTv3r+ZdzzwszucNB1oY9uzUQsD/LZjz6O26vqUt7sVJBnkmWyeX72/EEOHmtBAj6PiyceXsWKJTd3ZoGUkqaBAXKmRW24CJcxOX/1Xv6319n3/EFKa4rRNA0zb/LSs9sJl4VYc++KSRmDMjWEEGyKPkCNdx5nEvVoQjDXt4RKT91UD+2msGfPHu69914AFixYQFdXF+l0Go/HQ0tLC6FQiIqKQhvRu+++mx07dvChD31oKoes3MSklHzr8AG2NZ3D53SiIfh69z4OdbbxJ7dtGPcN/Lbt9fT1JSkrHb4x7+9P8stfH+QTf7AVGM4UfDdNaOSlNarz1FZEONfWSzjoHXotmc5RHg2gX1wQOt83wPm+fsqDAUQoSNXswkNBRzzBWTPJvDFfpaJMLDVPKNOJZdv8r327ONTZQdDlwpaSw50dPDh3Ph9eNv4SEr95/jC5nEnpO5rKdHXHefnV4zz5RKEYviXty85HQghMaV/zHE6HTnGRj1Qmj88zXJNtMJllfs1wgOhEZze9yTQVwSAEg9QsKPw764gnaMklKaVozNepzAwqyDPJfvKbAxw41kJp1I+maaQzOb7zkz38achLTdXNWe+lM5Hgf+3cRcdgAgE4NJ2P3raa26urb+h5LdNi96/2U1wZQbu4kms4DAJhH2/+dI8K8twChBBUe+dS7Z071UO56XR3d7No0XBnhkgkQk9PD9XV1XR1dRGJDH+fRaNRurouXwy2vr5+TOfPZDJj/uxkmyljnSnjhEvH2pFO8VzDcYpdLoSVQQJ+KdneeJp56NT5x1fk/803j6Npgv7+4WL7UkqOHDnHkSMlOBw6UkqMtMWFZCc+vbBKapomPQO9rLFLL/tna0ubHisBQLEeYEGFi4Mn4gzGB/G4HGTzJtmcxcY759PQ0ADAyb4BkokkMcsccaxUJsuxxrNU2+Yl5xmNmfL7nynjhJk11htBzROjM1PGCTNnrJcb5+l4jF1nz1DiciOtNALwSsnPjx6m1rSJutxjPp9tS/bvP01RkXvEPCGw2bnzBEsXFzJv8tIim0zTkczi0gqP4XnTJBZPEtSty/7ZmtKmxxzEEBpR3c+K2gC/2NGI26njchiksnlsKZlfWjX0+WMd3QwmEnjeNR/EU2mOn27Em4hf9zXOlN89zJyx3shxqiDPJBpMZDh0vJXSaABNK0RxPW4n6XSeN/eduSmDPLaU/MObu+hLpSjz+RBCkDFNvrH3LWYFQ1SFblwL9XzOJJ/Nozv0Ea87XA4GB5I37LzKzcu2JbZtYxj6td98k3M4HCP+X0o5tDp1tZ+92+LFY+tyVl9fP+bPTraZMtaZMk64dKw9zefx+31EAiPnlNRgHBEJs3ju/HGdr6zsPOl0bmRtBdNC4mTp0iVDWTafSZTwv0+9RMbKIRAMJrNsqFzEE/PuxqGN/N5oSnbz7XOvEjNTICVFws9HV9/DX86dxwu76mlq72NONMgDmxaz4B0rtCWJJL9u6SDg96FfXMCQUpLSBrlj+VIW14wtM3im/P5nyjhhfGPdv3//BI9m8ql5YnRmyjhh5oz1cuOsbzhOIBAg/K6gfy4xiKOkhMVVY99VIaUkEq7H53fjeMdzRyaTJxQUI8byJwMh/rVxGxlpoQGDiSwPzl7DQ7UbLumEVR9r4YdNr5O2ckgpqTTC/N4d97Jw/jx+u7uBzt5BFs+P8ODGRdSUh4c+5ywp47XOHkKBwNC/q8I8YbBx+VLml1x/2YKZ8ruHmTPW8Y7zavOECvJMomQqiybEUIDnbU6nTt9NGnQ4399P52CC8sDw3lG3YYCU7Gpu4cnlS2/YuV0eJ5XzKuhr6yMYHf5Cj/XEWfvg+NIypZSkExks89qplcrMZ1o2r+w7yav7G0ln89SWh3ni7hXMrrx1uxOUlJTQ2zvcgrOvr4/i4sJNQ2lp6Yif9fT0UFpaOuljVG4dfqfrMhulQAAh1/hrD2zaOJ+f/vwt3G4nmiZIaTmOa23413r47vk93FuxiCpvmDp/CV9c/jhH+puJ59PQneTB+RsvuXFPmVm+3vgCGoJSVyEwFc+n+PqZF/mLpR/kE09suuJYiv0+7lswhxdPNhJwuTCExkAmzZxolJVVFeO+VkWZKGqeUKaTIrfnck1XkUDA5bz0B9dBCMHtt89l++sNlJWFEEIQ1zIcc7dRvqiIH57bx9aKRZS4AywrquaLy5/g8EAzaTOHoyfNvbW3XxLk7MnG+ebZV/DpTkpdQaSUdGfi/MuZ3/K5JU+wsO7OK45nTjTMmlmVvNVygZC7kKEUy2RYM6uSecW37r3rrURV/J1E0bAfh1Mnmx2ZOpdM5Vg0r3yKRnVjZfIml7vz1jWNRPb621hLKWlLxjkb7yNnXb3GgRCCRz/9IJZl032hl8G+BF2tPfiKfGx9avN1n/ttx3Y28Pe//zW+/KGv8OznfszrP96FbU/fYI9p2RxsaOH//GI33/71PhrOdyLlZWa5G6ynL8Hre07z2q6TXOgYmPTzj8evdxznVzuO43TqmBGLV1KN/Mmvfsa2s2em5M9yOrjzzjt55ZVXADh+/DjV1dW4L95IlJeXY5ombW1tWJbFa6+9xp13XvlmRFHGa2lJKRGPl95UEiklUkr60mn8Thcry8Yf+Fi/bg6bN86nt3eQ1lgf2/ynSdTkCZR72NN9ji8feY7T8U4AAg4Pm0sX8nDVKupckUsCPAAN8VYyVo6AY7g7V9DhJWVmaYhfuOZ4fmf1Cv5o4zoqQwGCHhdPrlzGf9y6GaeusgyV6UPNE8p0cltFJW7DIJbJDM0T3ckEpV4fCyPjb8hx/33LWLGihu7uQc4neng90IhVC66og9c6TvHlI8/Rlirc/4ZdPu4uW8zDVSupcoYum8V2sP8sFjYeo7BQIYQg4vLTmx3kfPLyWxvfJoTgExvX8dF1qyn2eYl6vXzkttV8ctN61XjmFqEyeSaRw6Hz6AMr+eEv38LpMHA6dRKpLJEiH7evvjlb2dWGi9CFIGdaOC9ucZFSkrMsVlZeX2CrN5Piq8d2cSbWiyYELt3g3y2+jXWlV67tU7Ooij/9x99n7/MH6TzfTd2yam57cBWB8Ni6j5w53MT//fLP8Id9lMyK0t3ZzXP/+ioAdz65cUzHvJFsW/Kd3+zjYEMrHrcD25a8daKZBzct4j1bblwW1bvtO3yeH/56P7ZdCIgIcYz771jMg3dN/1a/qUyO1w+doTjs54ijgy6RwKHpZPMmf73/FQZEmvfPXjbVw5x0y5YtY9GiRTz++OPous6Xv/xlfvrTnxIIBLj//vv5whe+wKc//elCsPXRR4eKayrKjeDUdf6fjVv4+oF9nB8YIG+aaIM2yxJBXkkfYcPm+ZSUjn17sK5rvP+xtdx15yK+3vA6dXmTWcHh1PhYLs0Pz+/nC8sfHtUNdNrKcbmlAYkkY+Wu+XlNCDbU1bChTnUiUqYvNU8o00nQ5S7MEwf30ZFMkMuauBKS8qSHV7JHWb9xHkVh35iP73Qa/O6HNtHdM8jf1/+WRaKCUn9h3gk43HRnBvl16xE+sWB0wcxEPo1+uZVyIclY+Wt+3qHr3D1vDnfPm3Nd16HcHFSQZ5KtX1VHNOzjzX1n6B9Isum2uWy8bQ5+39S2skvG07Sd7cTjc1M5t3SoUPF4+ZxOPrx6Fd/afwBdCAxNI22arK6sYHn56IM8Ukr+4cibtCZjlHsL+0vTZp6vHtvFf1kfoNp/5SrxxVVRHvmD+ybictj+o524vC68gcLqq8NlEAr52faj3Wx+/3r0aVar5UxrD4dOXqC8eHhPrmXZvLz7JBuW1xENjX0yG63BZIYf/+YAoYAHp7PwlWNaNr99/QTLFlZSVT69K/zHEoUVnwEjTZdI4pdOBAJd0zByGr88f4K7KucQdnmvfbCbzJ//+Z+P+P+FCxcO/fe6dev4+c9/PtlDUm5hFf4AX7xjK6dau3j2X7YhEzY5b5rd506zb88Z/uBT91BTO77V2nDYR5eRoMw1MmAUdLhpTvaRs01cuuMKnx5W6ytFo1B4+e1Mn0J3Lqj1Xb2FrqLMJGqeUKaTueEIf7P1AQ6eauF7z76JIwdJT5JtZ0+wd1cjn/zM/RSXjK9eaFHEy4CRptw98jhFTi8nBtpHfZxFwVm80X1iRL2qvG0hEFR7x595pNzcVJBnCsytLWFu7fS5idv5mwO88K3thdRFW1JaHeUjX3iccFno2h8ehTtn11FTFGJnUzOpXI7VlZWsrKzAuI5AUksiRtNg/1CAB8BjOIjlMuxsb+Kp+ZMTKOhu7cXjHxmQc7odxHriZFJZfMHp9aB/trUHIRixsvx2gdDm9v5JCfKcberBsuVQgAfAuDiGk2c6pn2QJxz0oGsabfYgmmCoRbJp2ZR4Cxlh5wf7b8kgj6JMN0IIDr1+Bi0FxRfnMH/ATSyW4rlfHOCTn3lg3OcocnoZyKVGFFLO2xYe3XFJceUrqfJE2FC8iJ3d9UNBoaxlcmfpUio8N18TBkVRlOlCCMGeFxrwC4NQaeHezR9w09M9yCu/PcZTH75yTbTRMISGz3CSsy1c+vC9b9YyCTtHf6+4IFjF0lANRwea8OpOLGmTlxaPVq0fsdVXUS5HBXlucedPtPKbb7xKuCyE4+JDeG/7AN/7u1/xqb/78ITt26wLh6kLh6/9xitImTk0IS4Zj6FpDOTS4x3eqNUumcWJXaeJlA8XaEsnMgSjATz+sbdevFF8nitkiAmBx33t1eaJoBUiI5f/mT79y4K5nQ4e3LCIf9qzEzNgYwtJLm+ha4KK4iD9ZhqfMb6CfYqiTJxT9W2EikbeAAeDHprO95LLmSMCzmPxYNUSvnFqBy7dwKkZmLZNdzbB+2tWXbb+zuUIIfhA9UaWhKo50HcGgWBtZC6LgmPv7gLQMTBIVzxB1O+lMhxUtRcURVHeJZczaW7qpbRsZJetUJGXU/Vt4z6+EIIHKpfwk6YDlLmDGJpOzjaJ5VM8Wbd61MfRhcZHZ9/D0YHzHB44j0d3si46nzn+sddxlVLS2hejP5mmvChAaXBs5SuU6U8FeW5xB149juHQhwI8AOHSIG1nO+lu7aO0enpUYK/xX6ztY5k4L0bFpZRkTZMV0Ru3hzuTynH6WCu5rEnNvFLu/p1N1O9ppK+9H3/YT3IgRVYz+dB/enzCtrhNpOXzK/jl60dJprP4PK7CtqPBNEV+N/NmTU6q57y6EpwOnVQ6h9dTCIbk8iaaJli2oHJSxjBe961bAC7Bl4+8QjqfpyTkZ1ZJEYNWlnKPn3khlTarKFNFSoltnsLKn0ZoASJRQWzAHNHG1sxbeDwOjAnYUrsuWsdAXYpftx7FtNMI4MHKJTxYeX01xjShsTRUw9LQ+Ovq5C2LZ984wL4zrWiawLZtlteU8wd3r8ftULd6iqLc2qS0sPPHscwmEGH8fomZt0Y8/+RzJoEJysi/v3IJKTPHK+0NSAoBmydr13B78fXVxzE0ndWRuayOzB33mJLZHF9/dS8N7d1oQmDbks0LavnQplVDGfbKzUPN/Le4dCKN7hh50yuEQGiCXObaRb0mi9fh5JkFq3i24QCGpmEIjbSZZ3G4lLUl41v5vJKm05185ysvkk3nQUoQgrves4pP/v1H2P6jXZw/1kpxdYQnPvk+5q+ZnoWzQ34Pf/SBzTz7q7109Q0CgrKIn48/umFCHnaktEnmjpLI7kVgEHBvRL6rP6XH7eSjH9jAsz/ZTSKVBVnI7vnge9dSHJkZKwhCCO5fuYCqmhDfOLGHWC5DXGaZHQjzyaUb0dRquaJMCSlNsol/xsrtASRIweOP2nz3u2sx83MxHDqWZdPbk+C+h1cUMgvHqbBKu5S7yhbQn0sRdHjwXmc2X288SW8sRXHIR2QCHipePnaaPY0tVBYVtjRLKTnS1MGvD9bz5Prl4z6+oijKTCVlhmz8/8My63k7tfyZp+B739uAplej6xpm3iIeS/Pge1ZNyDl1ofFE7RoeqlpGLJ8m4vSOql7bO3X0DRJPZqiIBgh4x79b4Cf7jtHQ1kV5qDBP2FLy+slzVEdDbF0y/iCSMr2oIM8tbunGBRzbeZpgxD+U1p1OZnB5nJTXTa/shHuq5lHjL2J72zkG81luK65iXVn1DWkZa+YtvvfVl9F1nZKKQt0ay7LZ9uuDzFtWxdOffT8A9fX1zF88PQM8b5s7q5gvfuIhOnri6LpGeTQwISn8Uko6B79JLL0dTXMikQxktmHq64GRK9oL55bzV595hMbz3di2ZHZNMcFpuL3tWpaEy/j7je+lLRXHoemUefxqO4SiTCEz+xZWdhdCrxr6t1gUjvHEB47w7LfLkbaGRLLpzoVsvXdiOwq6dAflnuurXZc3Lb73ykH2nWxBv3iTvXFpLR+8e3wrqdvqzxH1e4b+DIQQlAR9bK8/xwfWLVPfU4qi3LLymVew8idGzBNlZd089lgD3/9hBIFAaHD/IytZs25i7+m9hvO6FwFSmRzfemEf9c1dF+cJeGDdAt6zYfGYv8vzlsWexmZKg8P3rZoQhL0eXqs/q4I8NyEV5LnFLdu0gIOvHef0ofM4nA5s00Zo8MxnH8WYhine80LFk7I15sL5btKJLNF3FJ/WdQ3d0Dm69yx1C8a+H3YqGLrGrLKJLXCcMc8Qz7yO06hAXKxDIaVJ0niNvPU7OPSRxcU9bifLF1VN6Bimgq5pV+3mpijK5LFyOxGad8SNr9BCVJSn+fxf3U4sFiZY5MU3xR0s3/bivpPsqW+iPBIcSpd/48g5SkJ+7rttwZiPm8mb+F0jHyR0oZGzrLcTURVFUW5JVvYNhBYeOU/oxcye08Hn/9/7GIzpFEV8eDzTo77ij7cf4URTJ+XhwqKsadk8v7ueymiQNQvGtnvBtiWmLS/JPNc1jWzOnIhhK9PM9HuKVyaV4TD4vb98goa3znLqwDkCYR8r71xMSdXkdvdIWzmOD5ynOxtnljfKomA1Dm3q/npKybs2HRUIChksCqRy9UgYCvAACFH4naXzjZcEeRRFUSacMArtZd/xkpQSicTjceP1j73g/0STUrL98BmKg/6hG21NE0SDXrYdPjOuIM+62bPYceo85aHhQqK9iSSraismZIuaoijKzGUA9rteK9zL+7we/P4b32l2tNLZPPtPtlBaNJxxY+gafo+L7YfPjjnI43IYLKwo5mxnH8WB4evtT6a4f/n8CRm7Mr2oII+Cbugs3TCfpRum5h95TzbGV0//hkEzhaBQS6DKG+UTcx/Ga0zNlp5Zs0vweF2kEhm8F7cVWZaNaVosX3d9RdNuVrq40qQo0MTM24qlKMrMY7juwMruRUoLIQpbd6Xdh6ZXIrQbV5R/rLI5k6Bn5PejoevEU5lxHfe9qxdR39ZFR2wQQ9PIWzYhr5sn1y0b13EVRVFmOsN1N7nkt0AMB06k3Y3uWInQpk+ABwpbeiVcknFjGBrJTHZcx356w0r++3Nv0D4wiKFrmLZFeVGAB1SQ56akgjzKlPtZyy7SVpZS1/AWmNZUD9u7jvJw5bopGZPh0Hn6U/fwnX/4LYn2AaQtEQI2P7icuoUza6vWjeJ3raY78T0sO4l+cZI0rQGE9OJ1Xl+XGUVRlLHQHatweB4hn3mhkFmIQNOKcPn/ZNrVoRFCsLSunIbmLopDww8WfYMp1swfXwOBIp+Hv3z/PRw430ZzTz+V4SC3zZmFzzU9th8oiqJMFcN9N5Z5Eiu3ZyhLX9OrcPo+NpXDuqyA10VZOEAsmSHkG14QiCUzbFo2vnpBleEg//mJ+3jrXCudsQSzS8KsW2xdBAAAIABJREFUqq3ENQ3Lcyjjp36rypTKWnlOJVopdo4sXlnk8LO/v3HKgjwAtQuL+cxfP8DZ4wPkMpK6+eWUzQqP6cFBSsnJhnbe2N5ALJZi4eJK7rhzIUVF02sF4XoYepjK0J/RHv8aObMTkBh6FGf+STQxPepfKIpycxNC4PR9CMO9Fds8ixB+NMdihJiewY3Htizj/I9fp7N/EKehkzMtAl4Xj2xYNO5je5wONi+oZfOC2gkYqaIoys1BCAOX/9NI6z3YVitCK0IzFg9lf04nQgg+dN9q/vFnbw7NE9m8RXk4wF0rx7+TIOBxqSLLtwgV5FGmlCYEGtrFttvDwRMbG9cU3aRLKelI/pa25PPYMoc+181s//so9Y69qv3unY38/Gdv4fU6cToNdu04zdFDzfzxv3+AUGj87XOnis+1lDnF/4Os2YRAw2XU0dB18qqfkVISz2UxNA2fY3o+iCmKMrNoegWaPv22Z71beSTAf/rwvbx+oJHtbzaQa41juNwceO0kdz20HPc0KfypKIpyMxFCIIw6NKNuqodyTbMronzhd+/lld0n2b2nEbNjEPw59pedYsu9S9CN6RecUqYfFeRRppRDM1gdnsv+/tOUOEMIUajJE8uneKxqxdD7pJT0ZhPkbIsyTxBdjL3V7LV0pbbRPPgT3EYJmghj2Vma4t/D0HxEPeuv+3i5rMkLzx8mEvHhdBb+ybndDro64+zbc4b7Hlg+0ZcwqTThwOOYN6r3NsUG+OaR/ZyPDyCANWWV/N7y1YRcqoaPoii3BrfDoPHVRlxdKcqjRUhb8vpvj9HW0sfH/vS+abfNTFEURZlcLjTOvtKIP5VjVnEEM2/x4k/309c9yOO/u2mqh6fMACrIcwuTUnIu3s+FRJywy82iSCmGduOCJ1fyvqrb6c4O0JLqhouFl1eH57KpuFDXpTeb4NkzOzgz2IUQgqDDw0fnbmZhcOJXbaWUtCWfx6VH0C5mEumaCwch2hLPjynI09+fxDLtoQDP23w+F2caO2d8kGe0YtkMf7P7dWxpU+7zI4EDnW30Z9L81eat6sFGUZRbwqljF+jpjFFSPlyHrqQ8xJmGdlqbeqiuU50JFUVRbmWH954lmchQXFYoZ6HrGiUVIfbvamTrwysoivqneITKdKeCPLeovG3xtSN72N91AShslCr3Bfjs2juJuCd3+5DPcPMn8x+lKdVFLJek1F1EubtQ+8aWNl87+SpdmTil7iBCCBL5DF89+SpfXPEYUddEf8nZ5O0Y7nel/WvCQ9buHdMRfX4XUkosy0bXh4NomWye4pLguEY7HUgpac/0cGawBV3T0Czzsu/b29ZKOp+nIlBo8SuAMp+fs7F+zg70MzccmcRRK4qiTI2u9gF4V1BbCIEQ0NeduGyQJ2lm2N1znGPxc3h1N5uLl7E4WKuC44qiKDehC829ON61OKxpGrom6OtNXDbIE8sl2NFzlNODrYSdAbaULGeuv2qyhqxMMyrIc4va1nqWfZ2tVPmCQzeJnelBvl1/gD9bvWXSxyOEoM5XBu+qQ9yU7KU9PUCZZ7gws9/hJpGOsa/nHA9VTWwWjBA6PqOOjNWNUx8+Z94eIOhcMKZj+v1u1tw2m317zxCN+tF1jVQqh5SSjZsmv22hadnUt3XR1NNPxOdlZW3FmDuwSCl5tWsPr3cfQEiBRJJKJnH3+1kVHllItDuVRNcu82BDIctHURTlVhApd2EU90LAgsEwb2ewAkSKL71xz1g5/vnMr+jK9OE3PPTnBvnWuRd4qGI995StmeTRK4qiKDdaaY2b+uZO8IchUQQIbFti2ZLwFQI8/3j6ZyTMDH6Hm77EIPXxZn6n+m7WRMb2/KLMbCrIc4va1nqOIpdnxCpgidvPoZ4OUvkc3mlSEDdpZi+7UmkIjVgudUPOWRN8koa+/0HWzGNoPvL2IAKNKv+jYz7m+x5bg9NpsHd3I5YliUR9/M7TG6isCk/gyK8tmzf5x5d2caq9e6j+UeAtF//h4TuoDF9/VlF7pps3ug8ScRYN1UnqTlv8qm078wO1+AzP0HvnhiO8eO70iM/bUmJLyazAzM9oUhRFuZaW5H6aS35C5M4O8nkTwwqQP7Ke/maYs7CcWXXFl3zm8MAZOtN9lHmG5wuv7uaVzgPcHl2Cz1A1zRRFUW4GUkoaB7czMPd5gnYnprQxshFyh26jv8Nk7ab5lw3y7Oo9TsJMU+IubAP26C6yVo7ftO1iRdFcDE0Va77VqCDPLcqWNu8OnQgACTZyCkZ0ebO8hS08pm0NfUFJKclLi4WhG9NJJeCcz5Lo52hP/JaU2UrEvZAK3wN4HWNPeXQ6Dd732BoefGgF2Vwev989JWn22xvOcrKtm4qiwND5+xIpvrPjAJ99712jGtNgJsv+1gv0JFMkXR3Y0h5RCNshDExp05RsZ0louN3j6rJKZofCnI31U+RyY0mbeDbLfXVzKfWpvcWKoky9ZDzNmz/fy5E3GnB6nGx87xrW3Lt8xFbbsYrn2jnU9yM8RhEL5xVxoamHvsFuWLSLjfM/zn2PrB7xHdyfSbOjrYmXu3aTFTkiThvHxXEYmo5E0pXpZ7Z/+ncVUxRFuVkMdMd5/ad7OLnvLP6wjy2P3cayzQsn5L6+O3uaE7HnCLiLWTgvTGtTN3GrB7FwP/et/Rh3PrBsxPs7UwnevNDEi90HcDkg4rTRL9ZXdelOBs0YA/kExa7Q5U6n3MRUkOcWtaWyjh+cOoLXcAx9KfVkkiyOlOB3uKZ4dMOKnF4erlrBr1sO4dIdGEIjYWZZFCpnadGN22fqc9QyL/yHE35cp8vA6Zq6f3a7G1sIeUcGmMI+D+e6+4mns4S8V18Rbu4f4L9v20Eym0MTGklXB6Kon2hFEfq7Vgne3QHNqet8dsMdvNJ0lp2tzXgMg6cXr2DzrNqJu0BFUZQxymVy/OtffJ/Opm6CxQESAyl++g8v0Hamk8c+9cC4j9+aOgQIDM0JLpi9oJw6WUbS7GFzaQXud2ybbR2M8d/2biOVz5MxssTppzeVZXVpJW7DQEqJlBL/O7Ilr+tacyYtrX0AVM+KXNIYQFEURbnUYH+Sf/7sdxkcSBKM+Olr7+f//s0veOjjd3HXBzaM+/hNiT04hBtNGHi8MH9xFbZdQcrqZUNFDcY72qef7Ovm797aQd62SBl5kjJGdyrD6pIKDF3DkjYCgU8fW7ZnJpOnpbUPw9Coro6O+9qUyaVm9VvUvdXzONLbQUNfN1IWakBG3V4+tmT67e9/pHIFs33FvNl1mpSV47ZoHeuic3Co1MPr5tA1bHtkppakkMX17no57yal5Nl9BzEtm4pgYXtVlkoac+20DAxQFylMAFk7h1fzUeurvOQYXoeT981bxPvmLbrkZ4qiKFPpxO7TdDR1U1YzvGXK43ex98XDbHn/eqIVRVf59LXl7RRCjJy3CnXJBKbMjnj9uw2HMPROFgQHyUk4mbEZzGU5H+tnQSRKbzbO/MCsodT863HmbBff+d5OMpk8AG63g488o1ryKoqiXMtbLx1msC9BycWgh8vjxO118er3d3H7Q6tw+8a3fTZvpy+ZJzRNA4sR84SUkn859hZhdzdhT5y0DQ0Zm3guxYVknFn+AD3ZOBuiS/AY1794f/hoCz/62T7MvIUEQkEPWzaUs3hcV6dMJhXkuUW5DYPPrb2LE31dtAwOEHF7WVlcgduYfn8lhBAsKapiyQ3M3LlV3LFwNs++cQCf24n2dgbXYJKls8rwu68+CcQzWZr7ByjzD2+tcuGlJDeH9lQLfl8hc8fE5qmah3Dr06Ouk6Ioymi0nGy/bDcTTdPobu0dd5Cn3LOEpsQepJRD2ZSmnUMInSJn9dD7claeuPkiC4tbkFIghCTskRyN1dCekRRnnawomstjVZuvewzJZJZv/tsOXA6DkuJCp8NUKsc3/20HT7xv3riuT1EU5WZ3/vgFPIGRgRzDaSAtm96OGFVzxxfkqfAspydzBpfmH5onclYSlx7Abwx3XuxOx/G7XqLY142UgqCAiAf2D9TQmuzF79LYVLyMhytvv+4xdHXH+d6P9hD0u3CFCh2X4/E0v36hgU0bV4/IJlKmr+n3RK9MGk0IlkXLWBYtm+qhKGMgpeTkqQ7e3H2aZCrHssVVbFg/B6/3ysGaDfNqaOzsZdfp5qEOvhVFAT68efU1z/f2Ht+3M3/e5s4VU+ms4MnqOehCJ9s6yBz/rHFcmaIoyuSLVoax8taI16SUSFsSvEyhy+tV4l5ApXclbanDaJoDKS1AsCryQRza8INBLHeaYu95smYR2sVtr0LkWBpox9//Xv5y6XvwjrHY8qnGDrJZk/DFG3cAr9fJYHeG5pYYa649FSiKotyySqqjnD3ahL9ouB2wbduFRiZh31U+OTrVvrW0pQ7Tmz2HrjmwpYkmdNZHP472jgyfWO4IAXc7eSvC23flukiz3N9DLn8nf7707jEvth493oq0JS6XY+i1YNBDb98A55t7mTendFzXqEwOFeRRlBlq2xsn+c0Lh/G6HRiGzvMvHeHgkWb++BP34HY7LvsZQ9f42J1reWD5fFr7YoS8buaVRYcCOFfjdzlZWVnB4bYOygOFBx5bSuKZDL+zehlLQ4XaOvWifuIuUlEUZZIs37KIV3+wk4HuOKHiALZl09c+QN2yaipmj/6mVkpJX2cMTdeGWqMDaEJnTfRpqn1r6UifwKl5qPKuJugsH/H57sxRou4gLYMWPkfhu9mWTiyZ4P7ayJgDPFCoxXP5MUPetC77M0VRFKVg/YMr2ffCIQb7k/iLvFimRW9bP2vvW0EwMvrFAMuy6euM4XrX/bqhOdlQ+vt0pE7Qk23ErRcxy7cKnzGyJk4sf4SAo4julInXUTiGZbvRtX4eqK0cVzZ9Jp3nSjWkrzSHKNOPCvIoygyUSmV56ZXjlET9Q2mTPp+Lzs4Yh4+2cPu6OVf9fGU4OKaW6R+5bRX9r++ieWAAKDwYbJ0/h411Ndd/EYqiKNNIIOzjD/7rU/zyn16muaENoQlWbV3KI7+/ddRdU1rPdPKTr75Eb0cMKcEXdVL+l1VEygqdTTShU+ZZRJnnynXJNOGgwucjZ0m6UkmEEEgpqfL72FhRN65rnF1XgiYElmUPdQyzLBtNCCrLRzcnSCnJ2wl04UTXpk+jBkVRlButtDrKx7/0QX71zy/T0dSDw2mw6bF1PPCRO0Z9jNOHm/jZ118jEUshpSRS5aP6L2rxX8yw1IWDKt9Kqnwrr3gMTRjUBUPk7QwDmfTFOUpSE/SzPHppTczrsXBhBdt2NGDbEu1ivc583kJogtpRFmCW0iZvJzA0D5q4/MKzcmOpII+izECdXXEk8pJ9sS6XwenGjmsGecYq5HHzFw/czdnePmLpDFVFoaGsHkVRlJmuvK6UT/zNh0gnMuiGhtM9+tXQZDzNs3/9S4Ch+j0tZ9t49m9+xWf+7hn0UdYxKPespiW5g8WRKLNDEbKWia5l8BpeilzjC6iXlgTZevciXn2tHu1ikMe2bLbevZhI+Nq3hLHsKc7Evk/a7EIInTLPRuqCj6tgj6Iot4y6pdX8yVc+RjqRweFyXFLL7Wq62/r57t8/h9vnoriiCGlLmk628oOvvMC/+6vHR72gUOm9nZ5MPSuLy0hbJjnLQtcSRFw1eIzwWC8NgDl1JaxdPZv9B8/hMHRsKZE23LmpDp/v2t/1PemDnIv/hJwdQ8NBpW8r1YGH0YQKO0wm9aetKDOQz+fCtuSIAp5QiLRHJqB2xNVoQjCv+PpbKVqmxd6XjrD7hSNkM3mWbZzPXe+/jUDR+PcwK4qiTCSP//q3RJ146wyZZJaSWZGh1wIRL31dA5yrb2Pe8uqrfHpYyFnH/OB7aIw/B4BTB6fmY2Xk342oyXA1XS09bPvBThoPnSdcFuKuD25k8e3z6e4exM5Y1FWGsQTMmhVh1Yoa6mqLaWhouOoxU2YHx/v+N5pw4TbKkFi0p17HlGkWhj8+qnEpiqLcDIQQeAOe6/7coe0N2LaN92LxZqEJgsU+mk6209XaR9koM2XKPCuo8d9Ja/JNoDBPeIwIS8MfGn3m6ak2XvvBTlpOXqCstpStT21izopa2tr68Ro6teVhNEOnZnaUNSvriA20X/OYsWwjJ/v/BYcexGOUYcs8LYnnAagNvm9U41ImhgryKMoEam/tY8+OU/R0xpm7qIJ1m+bhH8MkcC2lJUHmzyvlVGMnJdEAmiZIJrMITXDb6roJP99E+NW/bmPvS0cIRvzohs7u5w9x+uB5PvXXT+O+SrFoRVGUmSDRnwLtMjfXUpAaTI/6OEII6gL3UuZZTSzfhC5cRJzz0LXRZRX1tvXxT//x25g5k0DET++Ffr7zX37MbR/YyMHT3dhS4nDoZDImIm/z8AMrRvVQ0JHcgcTGqRe2dQkMPEY5PekD1AXfj0sf3+qxoijKza6/J47DNfLxWwiBEIJUIjPq4wihsajoCap9WxjMt+LQfIRdc0edLdPccIFvfO7f0A0dX8hL66l2/uU//V/WPbOFvUcuoGsami7IZU28LoOy+4KjCvJcSLyEprkxtMICriYcuI0S2pKvMivwILpQnXcniwryKMoEOVV/ge987TWEJnC5HZxv7GTfm6f55H94iGCR99oHuE7PfHADP/3lfo6duABAUcjLM09toLTk+mvt3Gi9HQO89eoxSmZFh/b3llRF6L7Qz/E9jazdunSKR6goijI+1fPLkfbIDEvbtgGNyuso3Pw2jxHBY0QueV1Km85MI+2p4+iak2rvSsKu4Y6GO36+j1wmT3FV4bMOlwPDZfDjH+5h6caF+PzDQfXWln727zvH5jsWXHM8abMTXYxctBBCQwhBzoqrII+iKMo1zF1ezZE3T8M7EnbMvIWuOUadxfNOPkcpPsel84slTTrSDXSkG3DrAap9qwg6hrspv/LdN9AdBkUXnxlCLgexfo0ff28PKzYvwHlxC5qUkob6dhoa2tBGkUiatrrQxchMWE0UuoSZdhJ9HAWhletz7ZY6V7B37142btzIa6+9NpHjUZQZybZtfvH9vXh8LqIlAfwBNyXlIWIDKXZuv3oK/Fj5fC4+8swm/urzj/LZP3uYz/2HR5g/t+zaH5wCPW0DaJo2FOB5m+HQaW3snKJRKYqiTJw5y2axcHUtXS19DA6kiPclGOhKsOHB5RRfrNEzXlJK9vf+hJ3d36Q5dZCzg7vZ1vlVGuNvDr2n6XgLvtDIhQXpMMibNoY+8jvY53Ny7GjzqM4dci3AtJMjXrNlHoGGx1AtdRVFUa5l+Yb5VM4poaull2Q8zUDPIIO9Se57agPeMWwTvhxLmuzq/ja7e75La+oop+Jv8Er7/+JC8tjQe5obLoxoAw+A20kmnRtR71MIgcOhU39xQflaQs4F5O34iNdMO41DD+DUpt8i9M1sTEGe5uZmvvnNb7J27dqJHo+izEiDsTSx/uSIFVKAQMBNw9HWG3puv89FNOq/JIAynYSK/di2PaKdMBRWL0qrLl2pVhRFmWk0TePpP3uYx//oHipqo1TPL+fB31vPwx/ZMmHn6Mmeozl1kIBRgs+I4HdE8Rphjg28QMYaBKC0ppj0u9L+pWmBEBiOkUuxpmnhG+WDRZlnAy49QjrfgWmnyVlxMv8/e3ceJVd53vv+u4faNVd19Txoas3zgAaQxAzGIDA2NgJPYMeOsXFiJyEJnJv4nHty7/Fa8b1ZuVlJHJzExNMBJ+4EY2OwMZjJgAxIgMbW0Bq6pVbPU83T3u/9o0WLRi00VXd1dT+ftVgL7ara+1eF6Lf62e/7vPluZgZuxdQLvyxZCCGmGsvj4gt/+TG23HsVlXVlzFsxk1u/tInNW1YX7BrtiT10pQ4RMqvxmxGCrko8RoC3B35K3skCUNlQQfp940Q+k8N0GWf8PmHbDn7/+Y0TDYEbMDUP6Xw3tpMmYw+StQdpDH4c7Tx7yonCuKgiT1VVFf/4j/9IICC76ggB4Pa40E5tS/teuWx+XJZqlZqamRUsWD2HnvYB8jkb5SgGuqP4gm5WbD73MgEhhCgFLstk3fXL+MI37uBz/+12GlfUo+tnftXqjyV56o1mvvur1/nNO4eIpTLndf7u9CF0dDRt+JwKUMrAUTb9meEZOVfesQE7b49sz5vL5Ih2DbFkaQP9A8mRYnsuZ5PJ5Ln8ivnn996MICsr/5T6wPUYmgufWcfiyJdpCNx4Xq8XQggBHr+bTVtW86X/+Qk+88AWZiysHrMvWudAjJ++upvv/up1Xtl7lFQ2d17n70jtxdI9I+dUAMoia2eI5joBuP5Tm0lEkyM3BDLJDNmBOPMW1zPQnxgZJzKZ4WuuuWz2eV3ba1azsvLPqfJejqYZhFxzWF7xdap8687r9aJwLqonj9crd2yEeC+P12Ltxnm88cohqmpC6LpGLpsnlcyy+bolxY5XdJqmcfcf3cyvf/wab72wl3zOZt6KWWz53NUEwlIEE0JMH8d7Bvm7n/6WbC6P22XyzuF2XninhQc+cQ3lwQ/+eejSvajhr+zE0hlauvqIpbNY7jiJ7lbuWr2IGQvr+fxf3cVT//obeo734fZZ3PS5a1h7yxr+47FtHDvag6Zr6LrGrbevYf6C81/m6zbKaAx9nMbQxy/pMxBCCHF2+9q6+OentuEohWWavN3Szku7j/AnH7sKn+eD+9pYug8bG4CBRIqW7j5S2RxuTxLVf5yPrpzBkssX8MmHPsavvvcCPSf68Id9fPzrtzBvwwIe/eGrdHUNoWlgmgZ3f2ojtXVlDJxH42UYLvQsKPvMJX8G4tKcs8jT1NREU1PTqGNf+9rXuOqqq8558ubm5otPVkTpdLpks48X+UzG9t7PZe6SAO0nArTs6wBNwzA0NlzTiK0N0dwcPceZpo4P+ruyYFMtczdUoxwH0zLpj3fT39w9wQknnvz/I4R4V9PLu0ApaiLBU0e8dA7EeGbHAT517ZoPfG29dxn7hp4jlkmw63gvGuD35nAcPy/vTZBOvMWXrt3Agsvm8kf/1Eg6mcFyuzBO9Vj40leup7s7SjKRoaY2jK/EdjZUyh4pcgkhxFTkOIofv/A2XrdFYKSg4+Vk7xCv7jvGhy774BnwswJrOZZ4k8FUnD0nejENDb8vSz5Tzi/3daLZ+/j4uuWsumYpK65aTCaVxe21Rmadfv1PPkzHyUGy2Tz19REsd2nt0yTjxLBz/lfbunUrW7duvaiTL1lSmjMYmpubSzb7eJHPZGzv/1xWrlpOdChJIpamoiqI5XYVMV1xyN+VM73/M9mxY0cR01w627b5xje+QWtrK9lslgcffJANGzaMes6VV15JY2PjyJ+///3vYxiyHltMb5lcnsOdvdSWBUcdLw/62Hnk5DmLPAFXBRsq7ubJw99DN2O4TRPH9pLt20xtKMz2Y+3cEUtQGfSjaRre9/VR0DSNmppwwd/XeMvkjtGX+DHp7D7ybpuB+F2U+W9DO8/tgsXEk3FCiIvTG00wmEhTUza6LUrQ6+adw+3nLPJUuGexKvJRftHyKC4rhctloHJhcgObqAl5+U3zYbasWozHZaLr+pjjRH1D6e2WmMo20xf/Mdn8EfKWTjR5L0HvDWMuhZsOZHQUosBCYR8hWYIkprAnn3wSt9vNY489RktLCw8++CCPP/74yONKKaqrq/nRj35UxJRCTD6GrmOZJnnbwfWeHUxyeZuA5/xm1dT7lmH3fIyhwUME3T6cbATQ0TUwdI3BZJrKoP8DzzHUn6CtpQuXZTJ3Sd2kviGRs7s5OfhNQGEadaB66E82YashKoOfK3Y8cRYyTghxcbyWiULhKIX+ngJFznYInOfsy7nByxk83kfK6cFjenFyEUDDNIZnCsXSGTyuDy4D9HUN0X6sF1/AzZyFdZfylsZdJneEjsG/RtO8mEYD0ElP/N9wyFDmu7XY8Yriooo8L774Io888ghHjhxh7969/OhHP+Lf/u3fCp1NCCHEJLRlyxY+/OEPAxCJREgkRm+rnEwmsW27GNGEmNRMQ+eq5Y089/YhaiNBdE3DdhwGEyluu/z8Z0AuqKlhZ1sP/vDpGUF520EpqA59cIHntV/v4VdNb6AUaCg8Pjf3/NFNF/2exuI4il3tnbx+5DgAG+fNYkVDzUXdUY2mXkSpLC5z+JcMDQuXUUk09TwR/8cw9NKbmTQdyDghxMUJ+jysbKxj19EOasIBNE0jl7dJZXNcvXzueZ9nYU0DLzZnqQmfnhGUyeVxmyZlvrPvlqWU4pmmN3j113uGuzZrUFYeYNNH5l3K2zpDzrZ5q7Wd7cfa8VouNs+fzcKayosaJwaTT4FmYhplAGh4MI1yBhI/I+y9CU2bvDcyxstFFXmuvfZarr322gJHEUIIUQos63TTvx/84Afcdtttox5PJpP09fXx1a9+lf7+frZs2cK999475rkutldRKfU5KpWspZITSifrWDnnh3UOlblpbu9E1zSUgvVzqynTUuf9nsrzefR8lpb2DkJuFznHIZ7Nc/WcOtqPHaX9fc9PDCY5ebCLoYEU219pI1zpxzSH+y9EY1Ee/uZ/8fH7NxTkM1VK8YsDrbx9sgfr1GylF/ccYMPMam5eMOuCz5d37UBpOTQGgOFlQEODUZSW4ED/m2iq4ZIzj5dS+Xs6HmScOH+lkhNKJ2up5ISxs66t93OyQ+fIiU40XUPTNK5eXI+W6Ke5eeC8zjvLdMimkxxJxAm4TbJ5h2Quz21L5tBy8OAZz4/2xulo6aKvO8HON08SqfaP9Onp7OjhmX8fIlzhK8jyJ9tx+MnuFg71RXG7dBxH8eyuZm6c18CmWRc+ayhn7QLyo8aJ6GASpfXR3PsWGqFLzjwexvPvqSzXEkIIcVYf1Hz/0UcfZc+ePXznO98Z9bjX6+XrX/86t99+O47jcM8997B69WpWrlx5xvnhseIoAAAgAElEQVQvtn9TKfV+KpWspZITJm/WtJ2hM92Fpbuo9dRwYP+BMXOuXL6MvmiCwXiKqrIAoQ+4q3o2Zl0Fj+7eQVvfEDOtCF9ctpwr5s864wv4W7/ZxRN/9yzKtumJZokm8pRHQkQqh+94Rsqgt3OIoZ4069avvbg3/h7H+gY4tH0/8xvqRpYaOI6ieTDOXbX1NEQubOZNf3wDA8kOLHO4R8TgwADhsiB5O8Psyssx9OA5zlA8l/L3tJR6t8k4cWlKJSeUTtbJnDORT9KT6cFreKh2V7N///4xs65dtYKugRjxVIba8hD+c+yq9X5KKagp4yd7d9I1GGe+r4o7V61g5cy6UeOEUoqXm7bxzA9eBKXo7M+QzjvU1pYTONUXqCysaD18kqpIPVV1ZZf0/gF2Hu/gZMZmQUPtSJacbfNmd5Q7r95E2HthY2JX9DKSmTcxjdPjRCjsRalqZjeunbT92y717+kHjROT8x0LIYSYFM7WfL+pqYnnnnuOhx9+eNQdW4BAIMBdd9018ucrrriCQ4cOjfnlXYipYs/QPp7teh5b2aAg7Aqz0jn7l7eKkJ+KcyytOpunj+/jv47uRLMgUGfST5QeK3ZGgWega5DH/+4pQuUBLI9Fun2IRCbO4XeOsfq6ZZjWqSnsGjiOc1FZ3u9oTz9KMaqXhK4Pz1g62jtwwUWekPc6oqnnyOe7MIwKFCly+Thl/tsndYFnOpFxQohzU0rxRv8OXul9DQBHOdR6aljqLDrra2oiwffsxHhh1/rfLdt5oeMQuk/D7zPooJ+YlT5jnDhx8CTPfP8FymsjmC6DaK6P7GCaQzuOsuq6Zei6PvwabbhgXwjNHd1YhjEqi8swUErR1jfIihm1F3S+iO82kpk3ydu9GHoZigR5J05V4AuTtsAz3vRiBxBCCFFajh8/zmOPPca3v/1tPJ4z77a0tLTwZ3/2Z8DwlNm33nqLBQsWTHRMISZMd7qHX3X8Gp/hpdyKUO6OkLAT/DazDUcVpnjyrq5UjP86tpMqr59aX4haX5AqT4Cfte2mIzk06rkHdxzByTtYp+4Al4U9aPpwH6ChvjgA6VQWl8ukesal350F8FnWqALPuzQNfNaF90UwjXLqI/8Dn3sdtjMEuKgKfoFy/8Xt/ComhowTQozWmmzjpZ7fEjSDRKwyyq0I3ekeXs9uL/i1DkV7eKHj0KkxYvifiNvHj1reJJbLjHru7lf2o+s6pmt4eW2kzAuaRi6bIz443EsrHk3hD3qoqitMD7SQx419lhsLFzNOWOZM6sv+Ox7XYmxnEAhQHfxDgt7rLzFp6ZqepS0hhBAXrampiWg0ype//OWRY4888gjf//73Wb9+PWvWrKG6upo777wTXde5/vrr5e6smNKaowcBDZd++stpyBWkzTlOZ7qLem/hdiY5ONSNUgpTP707l6nrKKU4MNRDne/0l3DlKBSn77wG/BbVlX5OnBhgsD+Og4Zh6Nz1levQ3KmC5FveUIPPchFNpQmdmnI/mEwTcFssra+5qHNaZh014T8AoLm3mZBvci7DEKfJOCHEaDsHd2Pp1sjPbk3TKLPCHI+fYCgXJewqXN+Y3f0d6Jo2quDuNkxs5dAS7WFNxYyR407ehvfU5SNlXgaH0nR3xRjojZPJ2FgekxvuXDHSo+dSrWucwS92HSCRyeJ3Wyil6EskqQ4FaKwsv6hzul2N1JUNF46be5sJeqf3OCFFHiGEEBfkgQce4IEHHjjj+H333Tfy7w8++OBERhKiqDJOGl0b48uvBlknV9BruXRjzMaXmgau930Bn79mDrquk8/mMS0TTdOorfSi57LcePcVhCuDLFkzm7KKQMGaP/rdFn9042b+5aU36IrGUSgqA36+fM2Gc27ZK6YOGSeEGC1lpzE0Y9Sxd5dB5Qo8TrgN46yPWfrox5ZtWsSrT7yJbTsYho6ua9RVevG64EN3X064IsDSy+ZwvP1YwfJVBwPcf+3lfO/VHSPjxMxIGfddsx5dv/TGzkKKPGISsh2Hls4+ktkcsyrLqAj4ih1JCCGEOKu5gUbeHtyFUup0E0knh650aj0XN3vlbJZF6rB0g2Q+i88cXoaVzGdx6SYrIvWjnlvZUMEtv38DT3/3N6hTvRR0Q+eTf3Yb625aPeb5HZUnnjuCUjn8rkZM/cLH4MbKCN+84ybaB4eXjzWUheWLuxBiWlsUXEBrsg2f4R0ZJ1J2Ci8eyq1IQa+1tnImT7TuIWPncRvDv+5Hs2kCLjcLwtWjnjtn+Syu/PjlvPrT14fHMDRMy+SL/3Mri9bPP/3E92zbaKssiewRFIqAay6G7r7gjCtm1PKtO2+mfTCK2zSpDQUKsnOXGCZFHjGp9ETj/MOvXqMnlhg5dvPqRdx+2RL5H18IIcSkNNc/h8XBBRyIHcLUzFN9eBTrrDV4jAv/8vtBgi43f7jkKv5p/6vEsjEUw3dtv7p4MyHrzN4nV95xOYvWz+fQjiPohs6CtXOpqBv7F4pk7jgHB75NzokCoGkGs4Ofpsq38YJz6rrGzPLRfX6yuTxvvH2M7W8fQ9c1Lr9sLmtXz8Y0pEWkEGJqWxZeSnP0ACeS7bgMF7Zjo2s66621Y88EvQR1vjBfWHg5Pzj0Bo5SgCLgcvP1ZdecMZNH0zS2/P4NrLl+OUd2t+L2WCxaP59QxdgNn6PZA7QM/DO2SgEauuZmXvhLlHmWXnBOl2Ewp2L0eJRMZdm2/TA795zA43Gxaf08Vi2bIb8HXiAp8ohJQynFd1/YzkAyRW14+AeL7Tg89dZ+5lWXs3zmhXVaF0IIISaCrul8pH4LyxPHaIkdwWN4WRJaSN/R3nG53rLyOv728o9xcKgbgAXhKjzG2ZtVVs2ooGpGxQeeU2FzcODb2CqLxxyefWSrDMeiPyRgzcFrXlpfIcdR/PA/ttF8sJNg0I1S8JOfbaflaDef/sQG+QIvhJjSLN3FXTM/zqHYYVqTbQRdQZaFFtNxuGNcrrepppGV5fUcjvViagYLw1W49LGXcWmaRv28WurnffDvWnknwaGBf0LX3HiM2lPHkhwe+g4rXf8Ll3FpfYUy2Tz//IOXae8YIBj0MBhN8sOf/I4brl7MrTeuuKRzTzdS5BGTRnc0QVvvADWhwMgxQ9fxuky2HWyTIo8QQohJS9d05gXmMi8wd+RYH+NT5IHhJporyuvP/cTzlNNOkHOG8Jinx1pDc5MD+lPbaQh+BBi+IdPe1kdfT4zyyiAzZlecV4HmSGsP+1s6qakOjjzf77N4Z89xrtm0kBn1hV2uIIQQk42pmywJL2JJ+PS26R2MT5EHIOBys6q8oWDnG8rsxVEZLON0c2RT95HKDTGU3Uuld3jWp+M4tB3pYWgwSU1dGTX1Zec1Tuxpbqe9Y4Ca6tPFIp/X4qVXD7B5wzzKQtLC43xJkUdMGnnbRoMzfgjoukY6ly9OKCGEEGIaUOQZtcXKCB1bpQHIpHM89shLHN7fMdzpWSnmLqzl079/DR6v9YHnP9k5BGr0GP9u09GOriEp8gghxCTnqBy8Z8fG09SpxyAWTfHDh5+n48QAaMM3BlauncOdn92EYZ69ITTA0bZeXK7RzzEMHU3T6OqOSpHnAsgiaDFp1JYFCfs8xNOZkWNKKeLpLOvnzfiAVwohhBDiUrhUPZpmYKvsyDGlHJTKU+Yenib/4jO7ObTvJJU1IapqQlTWhGg50Mnzv9p9zvOHgp6z3skNBArbt0gIIUThBa35gI6jTt98V8pG0zSC1gIAftH0Bp3tA1TVDo8TVTUh3nnjCG++euic5y+P+LFtZ9QxpRSOUgQDZ/acE2cnRR4xaRi6zu9du55M3qZjMErXUJyOwRirZtexdm7hphqK85fK93A0+ji7ev+WI0M/IZnvKnYkIYQQ40DHy+zgp8jZ/aTznaTz3aTznVR6NxK0FgLwxquHKK88vQOKpmmUVwZ489VDKDXW3d3TFi+oJRjwMDCURCmFUor+/gQVET8LGqs/8LVCCCGKz2PWUO+/jYzdQzrfNfyP3UWt/2a8Zh2ZdI69O49TXnW69YamaYTKfLx+HkWey1bMwuUyicbSw8UdR9HTF2fOzArqasLj+damHFmuJSaVhXWV/NXWD/HWkXai6QwLaitY0lCNoUs9cqIlcyfZ1fe3OE4WQ/cSyx2lK7mN5RV/TNCaXex4QgghCqzKtwm/azb96e3YKk2ZeyUhaxHaqZ1f7LyNpo9elqXrGnbePue5PW4XX/7c1TT9fAdtJ/pQwLw5Vdx1+zrMc0zhF0IIMTnUB7YQdi9hIP0OoIh4VuN3Dfeie7eAP1brjfMZJ8rCPu679yqafr6D7p4ooLF8cQOfuO0yac5/gaTIIyadiN/LDSvmFzvGtNca+wWOyuNxDd9hdREkYw9wLPZTVlT8cZHTCSGEGA8+VwM+19izZ1eta2TH7w5TVXO6KWZ/b5zV6xvP6wt4TVWIP/zidcTiwz1+ZPq9EEKUFk3TCFhzCVhzz3jM47WYu6CWtmM9lFcMz+ZRSjE0mOTGW1ed1/lnz6jgT+//EEOxFJZp4vN9cL83MTaZHiGEGNNgphnLKBt1zNLLGMocRCnnLK8SQggxVd1422oqqoL0dA7R2x2lu3OI8soAN31kzQWdJxjwSIFHCCGmoNvv3oDXa9HdOURPV5Seziiz5lSx6dol530OTdMoC/mkwHMJZCaPEGJMlhHGVll07fSPCUdlcOlBxt6BRQghRKlrTwzRmYhR7vExJxgZNUMnGPLyBw/dyoE9J+juHKKqJsTi5TOw3K4iJhZCCDFRlFK0xgbpSyeo8QWZERjdK6eqJswff+N29u06zkBfnPqZ5SxYXI/pkmW5E0mKPEKIMTX4b6Rl6FF0zYWuuXBUnozdx5zQx2VdrBBCTAHvNkvWNI284/Dwnm283nUcTdNQSrE4Us3XV2zC5zp9N9WyTFZcNqdIiYUQQkwkx3FGvvcnc1n+YfdrNA90j4wTG6pn8qVlG3Dpp4s4Hq/FZZfPK1ZkgRR5xDjqzw6yZ3A/0XyMRv8sFgbn4tLlbl+pqPFtJutEaY//GoUDaDQEbqLBf32xowkhhLgEyXia55re4K2X96McxcpN8zk5L8sbDFHvD6Of+vK+b6CLn7Ts5vNL1hY7shBCiAk02Bfj1//+O/a8fhjDNGhYXMZrN0fZO9BFvS80UuTZ1tXK7GAZt845/+VYYvxJkUeMiyPxNv7zxC+wlY2pmewabGaGr45PzvwoliHrK0uBpmnMCm6h3n8dWXsAyyjD1H3FjiWEEOISOI7Dj/7mKU60dBOpGf6ivvO1Q7wWTbBkw3z092yPXuMN8tvOo3x20RpM2eVSCCGmhWw6xyPf/BlDfXEi1SGUo9j92lH2hbtYvXzOyMweTdMo9/j5zYnDUuSZZGTEFgXnKIenO36DW3dTYZUTdoWosMo5njzJ7qH9xY43ilKKlt4+th1r41Bv38jUdXGaqXvxueqlwCOEEFNA6/4OThzuprK+DNM0MAydytoyUrkcycHkqOfqp5ZxOTI2CiHEtNH81lEGu2NU1pZhGDqmyyBcHSCRSJOKZUY919Q0sk6+SEnF2chMHlFw/dlB4vkE5VZk5JimafgMH/tjLawtX1nEdKelcjn+4ZXfcaCnF5QCNBZWVfC1Kzfis2RZmRBCiKlnsC8OijN6q1X2aPQkE1RzeuzuSydYVVGHZUjDTCGEmC56OwbR9NFjhKHpVA4ZdCViBMv8I8f70klunDF/oiOKc5Aijyg4S3ehUCilRn2JtJWNR3cXMdloT+7bz/7uHupCwZF1pQd6evnZ3mY+tWZyFKKKpTeeYN/JbgAW11VRHQwUOZEQQohCKK8OgcYZY/SMdg0nEOZkYghTM7CVQ8jy8OmFq4uYVgghxESrbihHOaNncCqlWNBuEdvooyMxhKEZ5JVDnS/IR+YsLVJScTZS5BEFF3IFmeOfSVuinTJX+NSuHTYZJ8uayIpixxvx8uFjVPr9o9aVVgX8/PbIMT65esW03UHqtZZWfrjtbWzHAYan63/q8lVcu2hukZMJIYS4VLMW1jJnST1H97ZTVjV8k2OgJ0ZdZZg/+dDt7Brs5Gh0gAZ/iLXVDQRck+fmjBBCiPG3aM1sqhoi9JwcoKwqiLIVg10x1l61nDuuv4EdPe20J6I0BiOsqW7AY0hJYbKR/yJiXNxWdyOPtz/NyVQXGjoacF31Jhr9M4sdbUReOby/jqNpGvlp3HtgIJHih9vepsznwW0O/3jI5m1+/PoultZXy4weIYQocZqmcdcfXc/TLzdxZOgNnJzO8sB6Fs5cht/jZmPtbDbWzi52TCGEEEViuV18+qEbePqVJo4ntqHn3Cxfs5i77r4Rt2VxTYPc+J3spMgjxkXQFeDe2VvpzvSStFPUuKvwmd5ixxpl05xZvHT4GHWh4Mix3kSSzXNmTttZPPs7e7CVM1LgAbBMA0c57O/okSKPEEKUOFvleT32Y5ylrSzRZ6BwSDvNdCTSwJpixxNCCFFkGTvJG+lHsVb1sdyYja1y9Mf2cTT7Bou9VxY7njgPUuQR40bTNGo8VcWOcVYfXbaEg929dESjnGpQQG0oyB3LlxU7WlFpjF3gmq6FLyGEmEo6UgfpzRwnbNaM/Fx36z462Ec810/AVV7khEIIIYqpNbGTWK6PsKv61BEvXjLsHvoNc4NrsfTJdeNenEmKPGLaCns8/I+brmd3Ryed0Ti1oQDLa2tGzWKZDk52DvLiawdoPzlIebWfXM4mncvjcQ1/Dpl8HkPXWVpXfY4zCSGEmOx6M23oGKMK95qmo6ExmOscKfIopTjc38/2E+04SrGuoYEFlRVS8BdCiCmuK30El+4ZdUzHBBxiuV4q3MPtNxylaO7u4Z2TJ7EMg/UzZzAnEhnjjGKiTa/fZoV4H8swWDujodgxiubY8T6+8/2X0DTweS1aDnZj5DN0OQrLbaJQGJrOvRvXUBHwFTuuEEKIS+Q3IyiGG+sr1Km5mxoKhcc4vST35837+dneZoxT2+g+e6iFWxcv4s4Vyyc+tBBCiAkTMCvoSB8E3t2JcXi8cHBGxgmlFD/Y8TYvHz2KS9dRwC8PHuKzq1dx/fx5RUwvQIo8QkxrTz+3G9PUCYeGp116PC70IY0qPcTlmxcAw1uoR3wyLVMIIaaCGb6lvHnyaZoPHSDelcc0DSKNLsp8lVRYMwDojMX4+b5mqgN+TF0HwHYcnj5wkCtmzWRGOFzMtyCEEGIczQuuZVfnS7S17SfZ5+ByG/jq86ytvBq/OTxT51BvH789doy6YBD91AzPrG3z4527WDejgZDH80GXEONML3YAIURxKKU42tZLKDj6h3Ao6OXkiQE2zpvFxnmzpMAjhBBTSLofjjxSQbI/j9k4iDO3g65EFyff0XFOzfA51NuHUowUeAAMXUcpxYGe3mJFF0IIMQFiJ+Do9yNkMlnMuQPYs0/SGxvk5G4HRw2PE3u6utBgpMADwyskHBQtff1FSi7eJTN5hJimNE0jEvaRzuTweqyR4+lMjkiZv4jJhBBCjJftL+4jM6Tj8rixo2XoaTe6o9Pja+GF4z/lxllbh3vTjdF6R9M0PO/rW5exczzf2cxrPYdQwKbK+VxftxSP4ZqYNySEEKKgXnl6J6S92KYbBky0tAcnl2GX/2Uae+tYX3UDXtfYP+M1pWGZxqhj8VyaZzv28GbfMSzd4OrqRVxdswhTN8Y8h7h0MpNHiGns+qsWMzSUIpvNA5DN5olG09xw9eIiJxNCCDEeOlr7MOdGUa4cRiKAZrvQlYEactMS20UsN8Cymmq8pkk8kx15XSKbxTIMVtTWjBzrSQ/ylzt/zPeOPMdANkresfn5iXd4+MDzI3d7hRBClJbOtl6Mxf0oXaGn/GjKQHdMVNRi98BrZJ00axvq0TWNdC438rqhdJqA22JRZeXIsbZ4Dw++/SP+ve23xPMJUvks/9H6Bv/76LZivLVpQ4o8Qkxjl1/WyEduXkUqnaO3L046k+ejt6xi/eo5xY4mhBBiHMycV03WG0WzT38FVApAw21ZxPID+C2LP9q8CQdFZzxOZzxOznH4w41XjPRZaB5q4//a82P2RY+SI017+iQd6U5qPEEOxbpoiXUX5w0KIYS4JDPmVZP1DqHlTs/cdBwHUzMxDJ1kPkZ1IMCXL99AIpcfGScsw+RPrtyMyxieofN6737+175/51jiJDknRVvqBH25fuo8Yd7oPUJXaqhYb3HKk+VaQkxjmqZx7aZFbF4/n0QyQ8DvxjRl6qQQQkxVa69dwsv/Giab78dSbhxbkc3kiNT40QwInmqqubCqkr+59RaO9PWjgLnlkeFlXEDesfn3tpdRaLg0Fx7djVKKoXyMoXwMpaAjNcTCUG0R36kQQoiLceUtq9j5Xy+QjXTjVib5vEMubTNjWTW6ruEzgwCsm9HAsppqjvQP4NJ15laUj/Ryi+dT/LT9NTQ0LMPCbVgopejN9lNuhdE1jY7UEDVeaeQ/HmQmjxACl8ugLOyTAo8QQkxxoYifL372c4QDZWTNBJoBMxdV4p+hMS+wgqArMvJcyzBYXF3FkuqqkQIPQEe6n7SdIeTy8m7zHk3TMDSDwVwUXdOIWL6JfmtCCCEKoGZmBZ+9/R78fh8ZPYlp6dQuCOGuViwv24Sln960xetysaymmoVVlaOa9bcmunGUIuDynpotOjxOaGgM5WI4ShGxpAfoeJGZPEIIIYQQ08iM+nq+XPXfeKv/BdqS+7F0D+HYIjZV3XZerzc1AwWEXF68pouUncVjuHBwSOVzzAkFWRKuH983IYQQYtwsnLuQ+xoeYkf/b+hIHyUXd9hYeQuLgmvP6/WmNnzjuNIK0Kr3kbZzuA0TpRSxXIZ15XOY5S8fz7cwrUmRRwghhBBimgm5yrm25hMjf25ubsbQzu9rYa0nQq0nQm8myoqyGRyO9dCXjpEjx8bKFXxp4fW4ZNcUIYQoaRXuWm6q+wwwPEYsCS0579fODdTiNz2k7CwrI8PjRH8mjoPNVdXLuHfulWjaGNs4ioKQIo+YtJRSdKaGp/PV+ULo8oNAiEnhmWee4W/+5m+orR3ut7Fp0ybuv//+Uc959tln+e53v0smk+Gzn/0sd955ZzGiCiHGgaZp3Nt4A/92+Nf0ZqNUeXxUuH3cXLeWG2pXFzuemARknBBienPpJl+YexPfO/Is8XyKGm+AOm+Qj8+8kg0VC4sdb8qTIo+YlDqSUf65eRtt8UE0oMLj477FG5kfrjzna4UQ4yuZTPKZz3yGz3/+82M+Ho/H+da3vsVPf/pTTNPkjjvu4JZbbsHvl7XXQkwVle4wf7bkE7QmuknZWWb6qgi6vMWOJSYJGSeEEDN9VfzF0rs5lugir2xm+2vwGlaxY00L0nhZTDo5x+Zvd71EZzJGrTdArS9IKp/jb3e9RDSbLnY8Iaa9RCLxgY/v3r2bFStWEAwG8Xq9XHbZZWzfvn2C0gkhJoqu6TQGalkaniUFHjGKjBNCCABTN5gfrGdxaKYUeCaQzOQRk86BwR76MgnqfKGRYyHLQ0cyytu97VxTP6+I6YQQyWSSl156ieeffx7DMHjooYdYvHjxyOM9PT2Ul59upldRUUFvb++Y52pubr6oDOl0+qJfO9FKJWup5ITSyVoqOaF0spZKTiitrIUm48T5K5WcUDpZSyUnlE7WUskJpZN1PHNKkUdMOvFchne3ZH2/wWxqYsMIMc01NTXR1NQ06tiNN97IV7/6VTZv3szbb7/Nn//5n/Pkk0+OPO5yuUY9Xyl11uZ6S5acfxO/92pubr7o1060UslaKjmhdLKWSk4onaylkhMuLeuOHTsKnGb8yDhxaUolJ5RO1lLJCaWTtVRyQulkvdScHzROSJFHTDqNoeE7O7ZyMLThFYVKKRSwqKy6iMmEmH62bt3K1q1bz/r4mjVrGBgYwLZtDGN4N52qqir6+vpGntPb28sVV1wx7lmFEEJMPBknhBBicpGePGLSqfEGuWnGQjqTMfrTSQYyKdoTUS6raGBhuKrY8YSY9r7zne/wy1/+EoCWlhYikcjIF3eAlStXcuDAAWKxGIlEgp07d7Ju3bpixRVCCDHBZJwQQojikZk8YlK6e+5qFpdV80rnUXK2zRU1s1lfNUu2URdiEvjoRz/KQw89xKOPPopt23zzm98E4F/+5V9Yv349a9as4etf/zqf+cxn0HWdP/iDP8Dj8RQ5tRBCiIki44QQQhSPFHnEpKRpGqsrGlhd0VDsKEKI96mrq+OHP/zhGcfvu+++kX+/5ZZbuOWWWyYylhBCiElCxgkhhCgeWa4lhBBCCCGEEEIIMQVIkUcIIYQQQgghhBBiCpAijxBCCCGEEEIIIcQUIEUeIYQQQgghhBBCiClAijxCCCGEEEIIIYQQU4DsriWEEEIIIQpGKcXRvcfZu+0QmgbLNy5i9tIGNE0rdjQhhBCTgOM4HHr7GM2vt+D2Way6egn1c2uKHWvKkCKPEEIIIYQomGd++DIv//RNTHN4wvhrv3ib6+/ayI2f3lzQ6/QmEjx7sIUD3X3Uh4N8aOF8GssjBb2GEEKIwnIch6a/e5qdLzXjcpvYtuKVn23nY/d/iPU3rSrotdqHovz6YAut/YM0lkf40MJ51IdDBb3GZCRFHiGEEEIIURCdrT389ontVNZHMIzhIo+dt3nhP7ex6polVDWUF+Q6XbE433zuRZK5HEGPm44TMd5sO8HXr9rIirraglxDCCFE4R3e1cbOl/dTPaMCTR+e4ZnL5HjyX59n6RUL8Ye8BbnO0f4B/vr5l1FK4XdbvHKsld+1Heeh665izhS/ISA9eYQQQgghpimlFI7KFex8rc3toNRIgQfAMA1wTj1WIE/vP0gqn6c2FMRvWVQF/PjcFo+9vQulVMGuI4QQ051SDgq7YOc7+NZRTFMfKfAAuO5TtCoAAB6nSURBVNwulKM4caijYNdp2rkHQ9epDgbwWxY1wQAAj+/eV7BrTFYyk0cIIYQQYppRyqY78Wu6k7/CdhKkzTIS2fvxW/Mu6byW2wVjtd7RwO1xXdK532tfVzdhr2fUsYBl0RWLE89mCbrdBbuWEEJMR7aToTPxM/qSLxGz+jg8cDn1wbvwmg2XdF6v343jnFmMVyjcHuuSzj1yLqU40NM7Uth5V5nXw/7unoJcYzKTmTxCCCGEENNMR/xxTsabMDQPbqMOR+ulZeBvSOUvbbbNwssasdwukrHUyLFENIXb52b+6jmXmPq0Cp+PdC4/6ljecXAZBh5T7mEKIcSlOh79Ht2JZzD1ELqqJJE9xOH+/4ecPXhJ512+eRGaBplUduTYUF+McEWQmYvqLjU2AJqmUeb1kMmPHicy+TwRX2GWg01mUuQRQgghhJhGbCdJT/I3uI1adM2NpmnoBAGH3sTzl3Ruf9jHZ//yDhzboefkAL0dAwDc+xd34A14zvHq83fL4oUkMlnSp77A522H7liCDy2cj8swCnYdIYSYjjL5LgbTO/AY9eiaCw0Ny6gk7yTpT2+7pHNXz6hg65/cSiqRobdjeJzwhbzc+42PDy/vLZBblyykP5EkZw8vNcvmbfqTKbYsWViwa0xWF3Wrw7ZtvvGNb9Da2ko2m+XBBx9kw4YNhc4mhBBCCCEKLOcMAQpdG/010ND8pPPHL/n881bM4sFHvsKJgx1omsaMhbWYrsLOrllZV8Pn16/hP3ftZSiVRtc0bl68gNuXLS7odd7PUQ49mU4cZVPlrsPUZdaQEGLqyToDaJqOpo1ef6trFuncpfdXW3nlYhZe1kj74S5cLpOGBbWjerkVwrXz5pLI5vhl80FyjoNL17lr1XKubpxT0Ou8n63y9KQ70TSNSncthjbxNx4uamR68skncbvdPPbYY7S0tPDggw/y+OOPFzqbEEIIIYQoMJceQcPAUTl07XSfHFvF8VmXF+Yalknj8pkFOddYNE3jmnmNbJozi4FUiqDbjddVuJ4/Y+nNdPFM5+PE81FAw6VZ3FhzO7P8c8f1ukIIMdHcRjUKB6UcNO108cVRWXxWYX7meXxu5q2YVZBzjUXXND6ydDE3LZzPUDpN2OPBPc7LeduTrTzb9TMyThpQ+IwgH669g2pPYZahna+LKpdt2bKFhx56CIBIJEIikShoKCGEEEIIMT4M3UON/yNk7E7yThxH5bDpR9fcVHqvL3a8C+IyDKoDgXEv8OSdPE93NJGxM5S5KihzlWNqJr/q/K9TRR8hhJg6LKOcCs/VpO2T2E4SRY6M3YFlRIh4SmsFj9s0qQ4Exr3Ak8zH+WXnf6KhUeYqp8xVQd7J8XTHT8g52XOfoIAu6p1a1umu1z/4wQ+47bbbChZICCGEEEKMr2r/zbiMMroTvyTnDOByFrOg/Iu4zapiRzunVDbHGy3H2dnWQdjn4cpFc5hXUzGu1zyZbiVlJyhznb6O2/CQtOMcjR9iRdnacb2+EEJMtIbQp3CbtfQmn8chQ7nnWmoCt2HqgXO/uMhiqQzbDrbSfLKH6rCfqxc30lAeHtdrtiYOk3dyBK3T1/GZfgZzfZxIHaPRP3G9gM5Z5GlqaqKpqWnUsa997WtcddVVPProo+zZs4fvfOc7Y762ubm5MCknWDqdLtns40U+k7HJ53Im+UzOJJ+JEGKy0TSNcu9Gyr0bAWjua8Zj1hc51bll8jZ/9/QrHO0ZIOC2yOZtXjvQyueuXsumRbPH7bpZJwtn7vh76rH0uF1XCCGKRddMqv0fotr/IZp7m5kZXlLsSOclnsnx1z97kd54goBlcbCjh9/uP8YffGgjy2bWjNt1s04GNcZAoZQaHkMm0DmLPFu3bmXr1q1nHG9qauK5557j4YcfHjWz572WLCmNvwjv19zcXLLZx4t8JmOTz+VM8pmc6f2fyY4dO4qYRgghStfezn6O9QzQEAmNHMvk8vzH73axdm4D7gI3eH5XjXu4AGYre6SJplIOAPXe8espIYQQ4sK82dpFXzxBfdnwOBEC4ukMj732Dv/31pvQde2DT3CR6rwz0dBwlIN+qo+RrYZ39qr1NIzLNc/monryHD9+nMcee4xvf/vbeDyF2w5TCCGEEEJMT+l8nu5knJxjn/U5LT1D+KzR/XfcLpNc3ubkwPj1xgm6wqyvuIpoboCh3ADR3CADuT4WBldQ65kxbtcVQghxWjKXpSeVwHacsz7nUM8QYe/oGkXA46Y/nmQoNX4zL6vctSwNrWEw10c0N8jQqfFibflmwq7IuF13LBd1u6OpqYloNMqXv/zlkWOPPPLIWWf0CCGEEEIIMRbbcXji8F5+1XoIWzm4DZOtC1Zw3Yy5Z2zfG3S76E6P/pKulMJB4XeP7/fQNWUbqfPM5FBsH7aymRtYxExf46iMSimaD3Tw2usttJ3o5OrNik0b5uHzucc1mxBCTGUZO8+PD+zk5fZjgCLgcnPPkjWsrzmzyB5wu4jnbd77Y9d2HDRNG7fZnjC8DPqqqptoDCygJb4fA4P5wSXUeUbvNOk4ind2t/H0M3sJvXSSNatmsWFtI26rcNku6kwPPPAADzzwQMFCCCGEEEKI6enpYwd44kgzNb4ALt0gY+f53r4dBF0W62tHfzlePaOSQwPHSWdzeCwXSim6ogkW1VVSHR7fZqCaplHnnUmd9+xbw7/4ygGeemYXXq9FKpHlmef28s7u4/zhl67H4xnfHcCEEGKqeuzAO7xw/Ai1viCGrpPMZfn2zm18Y8P1zC8b3Xh/w+wanjxwEp/bwjINHKXoisbZvHD2GTNBC03TNGb65jLTd/Zt5p946m1e/V0Ljp0m71j87Km32dvczu9/7mpM46IWWp2hMGcRQogSopRDzu7FduLFjiKEENOaoxRPHztAldePSx/udeM2TEKWm6eOHTjj+XUhP1+8bj2ZvE1XNE7nUJzF9ZV88br1Ex39DMlkhl8/v5fKigDhkBePx6SmJkRXd5R3drcVO54QQpSkeC7Db9uPjRR4AHwuC1M3+HXroTOeP68yxCc3riSWztAdjdMdjbN+3kzu2rhqoqOfoac3xu/eOExNdQi/zyLgd1NTHeLw0W4OHe4q2HXGd7N4IYSYZFLZffTEHiFv9wLgd19OZfBzGLq/yMmEEKI4co5Nc7KXPUffptLjZ13lLIKuiem5mLVtkvkcYWv09TyGi950cszXrJs3g1Wz6+gYjOGzXFSGJsfP766eGEqBaRqjjrvdJocOd3PF+nlFSiaEEJcm49hs6z7KicQg9b4wl1XMxGtOzOzERC6LgpECz7u8hkl36swbtpqmcf3y+WxcOJueaIKg103E752QrOdysnMQTddGNX/WNA1d12lt62PJwrqCXEeKPEKIaSObP0nn0P+LpnlxmXUoZZNIb0OpNLVlsgRVCDH9pPI5/r+9z7Orp5VQOoSjHJ5o282fLrueWYHxbxTpNgxmBEIMZtKE3lPoGcymWFt99t1IXKbBrMqycc93IQJ+N47toJQa1acnl7OpqJgchSghhLhQA5kk/9L5NtkBA13TsZXDz9t28+CKG6nwjP/PtnKPD6/pIpXPjSosxXIZrplx9mVRXss1KccJpcbYZt1RlIV9BbuOLNcSQkwbsfRLKOVg6MNbKmqagWnWk8y+Q84u3BRJIYQoFc93HKQl2kul6aXGG6TOFybv2Pzo8BtjfhEtNE3T+PSi1STzOXpScRK5LF3JGC7d4KNzl4779QupqjLIwgW19PTGcJzhzy6eyKDrGuvWNBY5nRBCXJyfte1mIJemzhemxhuk3hdmIJPiP4+9MyHXd+kGn160iv50ir50kkQuS0ciSpnbyw0zS2uGZOPsKmqqQ/T2xVFKoZRiKJrC63WxfGnhtlmXIo8QYtrI2d1o2ugdTobvturYzvhtvSuEEJPV73qOUmZ5R808iVg+jsb6iOUyE5JhWUUN/2PD9ayrmUHIcnNNw1z+6oobaAiEJuT6hfTpOzewctlMevviDAymcVsmX7znKqorg8WOJoQQF+WN3lbKzNHfnyu9frb3tU3IzQCAK+vn8H+sv4al5dWE3B62zFnE/3n5DUQ8k2MZ1vnSdY0v3nMV8xqrGBhK09MbI1Lm477fu4aAv3C7MMpyLSHEtOF1LSWZ2T7qmFI5QMNlFGYNrBBClBK3YZ5RzFEMF8Df3/9gPDWGy/nKissn7Hrjxedz89m7ryCRzLBnTzPr160a1XtBCCFKjUs3SL+vmOMoNdIsf6IsKa9mSXn1hF5zPJSFfXzpc1ezfUeYefPmUxb2jbrRUggyk0cIMW0EPJtxGXXkciewnTh5e4Cc3Ul54BMY+vhuvSuEEJPRtbULGMqmcU59gVdK0Z2Osbq8Ab9pFTld6fL73ISCbinwCCFK3nW1Cxi00yOzdpRS9KTjXFMzv+DFienE77OIlPnH5TOUmTxCiGnD0H3UR/470dRzJDLb0fUgYe+H8Vmrix1NCCGKYmN1I4ejvfzyyC6yqeFlq7P8ET47b3y3JD/RMcD2na0kklmWLapj+aL6M3alEkIIUXxbZizlrWMHOZmKoWvDs3iWl9Vx+6wV43ZNpRRH23p5a3cbedth5ZIZLJ5fK4Xz8yRFHiGmMEc5dKbbSdtJKtxVhF3lxY5UdIYeJOK/g4j/jmJHEUKIojM0nc8tuJx5KRfe+irCloe5wUr0cbw7++bOY/zk5zvQNA3T1Nmxu5XF82v5wt2bpNAjhBCTjGWYfLJqKYFZdfSk41R5/Mz0R8Z1Fs9zv23mVy/uw2XoaLrGmztb2bBqNnfdvk5mD50HKfIIMUXF81GeOtnEYLaXU5MrWR5ey6bKG9A1WakphBDitAqXlyWVM8f9OulMjp8+/Q5lIS+WNfw1VCnF/pZO9h48yaql459BCCHEhdE0jVmBCLMCkXG/Vv9ggl+/1ExleQDTGP6dxXEUb+xsZcNljTTOrBz3DKVOftMTYop6sfuXDOX6KLMqiFgVhF3l7Bp6kyPx/cWOJoQQYppq7xwkbzsjBR4Y/uXBY7nYe6CziMmEEEJMBq0n+gFGCjwwvCuVjkbLsZ5ixSopMpNHiCkomY/TnjpG2Dy9PEvXdDy6j33Rd5gfXFrEdKLUPfzww7z22msAOI5Db28vzzzzzMjjAwMD3HzzzSxcuBCASCTC3//93xclqxBicvFYLpRSKKVGTbnP2w4BvzR6nipknBBCXCyPe+wShULh98g4cT6kyCPEFGQrGzXGcV3TyTm5Cc8jppb777+f+++/H4AnnniC7u7uUY8nk0nWrl3LP/3TPxUjnhBiEquvDVNXHaa7N0Z5ZHjb2Ew2j1KKdStnFzueKBAZJ4QQF2venCoCfjdDsRThoBeAZCqLaRosW1Rf5HSlQZZrCTEFBcwQEVcFSTs+ckwpRcpOsDC4rIjJxFSSy+V47LHHuOeee0YdTyQSRUokhJjsNE3j83dvpLoqSE9fnJ7+OKlUlk9+dB31tWXFjicKTMYJIcSFslwmX/r0lXg9Fj19MXr64jiO4vfu3kg45C12vJIgM3mEmII0TeO66lv5xcl/ZyDbi6bpOMqh3juLxaGVxY4npohnn32WzZs34/WOHnCTySRHjhzhvvvuIxqNcu+997Jly5Yxz9Hc3HxR106n0xf92olWKllLJSeUTtZSyQkTn/XmK+vpHYiQy9lUlftwuZLndX35TEuLjBPnVio5oXSylkpOKJ2sxcj5sRtm09OfwHEUVRV+nOwAzc0D53ydfKZS5BFiyqr21PHJWfdxNHGAWC5KrXcGM32NGJpsTyvOX1NTE01NTaOOfe1rX+Oqq66iqamJv/iLvzjjNXV1dXzlK1/hIx/5CENDQ9x9992sXbuWmpqaM567ZMmSi8rV3Nx80a+daKWStVRyQulkLZWcUDpZSyUnXFrWHTt2FDjN+JFx4tKUSk4onaylkhNKJ2up5ITSyXqpOT9onJAijxBTmM/0syx8WbFjiBK2detWtm7desbxVCpFR0cHCxYsOOOxmpoaPvaxjwFQXl7OsmXLOHr06Jhf3oUQYqKl7DRvDeymOdqC13CzNrKSRcF5oxpBi/Mn44QQYqqJ5eJs799JS+IYYVeQ9eWrafTPKnas8yY9eYQQQlywvXv3MmfOnDEfe+211/jWt74FDH/J379/P42NjROYTgghxpZ1cjza+jgvdm8jkU/Sle7lP088xcs9rxc72pQj44QQohTF8wl+cKyJ3/W9RSqfoS1xksdan+Cdgb3FjnbepMgjhBDigvX09FBdXT3q2De/+U2OHz/O+vXr6e/v55Of/CT33HMP9913n9ydFUJMCvujh+hO91LlrsBreAiYfiqsCNv6thPPSzPgQpJxQghRit4e2EMsH6fCXY7HcBNyBQm7gjzf/UrJ7FIsy7WEEEJcsFtuuYVbbrll1LG//Mu/HPn3d+/QCiHEZNKWbMelu0YdG+5Vp9Gb6Sdg+osTbAqScUIIUYqOJtrw6qObxVu6RSKfYCgXo9JdXqRk509m8gghhBBCiGmhzBUm7+RHHVNKoXDwm74ipRJCCDFZlFlhsio76pijHBTgM0pjC3cp8ggxjQ0OJenoGiKft4sdRQghhBh3y8OLMXWTRD6JUgpHOfTnBpjtm0GlNfnvzgohhBhf6yKrsJVNyk4DYCuH/uwAy8OL8ZmlUeSR5VpCTEPJZIamJ7azd/9JdF3Dslzccdsa1qwsna7xQgghxIUqs0J8ctZHebrjeQayA4DG4uB8Plx77Vl318o7Dq93t/LbziP8/+3dW0yUdx7G8ecdhhkQGAVBCoqydWttQ12smF3PbKxp1MZEtkRxo22M2bqmbdpkt6mtDW1ak+JFA/GYuohN66FM221i2oaolaiJoPVGoKhRuwUrgqAgjCBWZi/Muuty6EUZ/vO+fD93MwyTJ8Pwf2Z+70lBaXbKw/rDmAlyu9hWCgBOkxqdrD+NXayyxnJd774hy7I0NT5D85Pn9Ps7t+/+rONXf1BF44/yut3KTpmoaYnjjF21kSEPMAyV/vOUvj/XoMTRcXK5LHXdvqN9/kolxMdoQtpo0/EAAAiZtBGp+svDf1b7zx2KdEUqOiKq38cGg0H942yFTjT+qDiPV5K0s7ZCZ1qu6K+Pz+Sy6wDgQJN8D+u3celq/7lDXpdXURHefh97p+euCquO6vvWRvkivbobDKqqpUGLxj+mZRMzhzD1f7EJAhhmWttuqfbcVSUl3hvwSFKUN1Jut0uVpy4ZTgcAQOhZliVfZNyAAx5J+lf7dVU21Sk1xqeRniiN9ERpbIxPp5rrdam9ZYjSAgCGmstyaWSkb8ABjyRVX7+q2tYmjR3hk88TpXhvtFJi4lR2+ZyauzqGKO2DGPIAw8ytW92yXFavrY+RHrdutHH5WAAA/uPHjlZJQbn+pzMty1IwGFRdR6u5YACAsHCurUnu//tuFWG5ZEnGeoIhDzDMJCbGyhMZodu37zxwfyBwW489mmooFQAA4Sc20iNLvQ/JclmW4iIH3roLAHC+BO8I9QSDff7MVE8w5AGGGU+kW0sWZ6q1rVMt1zvU3tGlxqabSh7jU9bUdNPxAAAIG08kpGikN1otXfeuxhUMBtXSFdBIT7SeSEgxHQ8AYNj0pDR5XW61dXfe74mmznaNjRmpib5EI5k48TIwDGVlpisxIU4Vpy6ota1Tjz+aoqwnf6MR0R7T0QAACBveCLf+PuWPKj5boR86bsiSNCE2Xmsm/17eCD5GA8BwF+8dob/9LlvFZyvV2HnvHDyPjRqj1ZN//8ChvkOJdgKGqfTxo5U+nitpAQAwkNQYnzY8uUAtt29JCmq0N4aragEA7pvoS9TG6Yt0rSugSJdL8d4RRvMw5AEAAAAGYFmWEqNiTMcAAIQpy7I0JjrWdAxJnJMHAAAAAADAERjyAAAAAAAAOABDHgAAAAAAAAdgyAMAAAAAAOAADHkAAAAAAAAcgCEPAAAAAACAAzDkAQAAAAAAcACGPAAAAAAAAA7AkAcAAAAAAMABGPIAAAAAAAA4AEMeAAAAAAAAB7CCwWAwFE98+vTpUDwtADjCtGnTTEcwjp4AgP7RE/QEAAykv54I2ZAHAAAAAAAAQ4fDtQAAAAAAAByAIQ8AAAAAAIADMOTpw927d7V+/XqtWLFCzz77rE6ePGk6Ulg4efKkZsyYoSNHjpiOYlxRUZGWL1+unJwcVVVVmY4TNs6fP6+nnnpKn3zyiekoYeGDDz7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      "text/plain": [
       "<Figure size 1440x480 with 3 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# create a random dataset with known B:\n",
    "X, Y, B = create_dataset(n=100, p=2, q=2)\n",
    "\n",
    "# find B_rrr\n",
    "B_rrr = solve_rrr(X, Y, rank=2)\n",
    "\n",
    "# plot X, Y, and XB\n",
    "scatter_plots([X, Y, X@B_rrr], [\"X\", \"Y\", \"X*B_rrr\"])\n",
    "\n",
    "print(f\"|B - B_rrr|²: {np.linalg.norm(B - B_rrr)}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 208,
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "outputs": [],
   "source": [
    "def evaluate(X, Y, B, method, **method_kwargs):\n",
    "    \n",
    "    n = X.shape[0]\n",
    "    \n",
    "    # split into training and validation\n",
    "    n_train = int(0.5*n)\n",
    "    assert n_train < n\n",
    "    n_valid = n - n_train\n",
    "    \n",
    "    X_train, Y_train = X[:n_train], Y[:n_train]\n",
    "    X_valid, Y_valid = X[n_train:], Y[n_train:]\n",
    "    \n",
    "    # find B by fitting to the training data\n",
    "    B_estimate = method(X_train, Y_train, **method_kwargs)\n",
    "    \n",
    "    # compute train and validation error\n",
    "    train_error = np.linalg.norm(Y_train - X_train@B_estimate)/n_train\n",
    "    valid_error = np.linalg.norm(Y_valid - X_valid@B_estimate)/n_valid\n",
    "    \n",
    "    return train_error, valid_error"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "skip"
    }
   },
   "source": [
    "<div class=\"alert alert-block alert-info\"><b>Try yourself:</b> Reduce the true rank $\\text{rank_B}$ in the following cell and see how the validation performance changes:</div>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 259,
   "metadata": {
    "scrolled": false,
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 1440x720 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_validation_losses(n=100, p=200, q=200, σ=0.5, rank_B=200) # try rand_B=5"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## More Recent Methods\n",
    "\n",
    "1. [Reduced Rank Ridge Regression (RRRR)](https://github.com/rockNroll87q/RRRR/blob/master/reduced_rank_regressor.py) [Mukherjee (2011)](https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3444519/) (combination of ridge loss and reduced rank regression)\n",
    "2. [Sparse Reduced-Rank Regression (sRRR)](https://github.com/berenslab/patch-seq-rrr) [Kobak (2019)](https://www.biorxiv.org/content/10.1101/302208v2) (combination of lasso and ridge loss and reduced rank regression)"
   ]
  },
  {
   "cell_type": "markdown",
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   "source": [
    "![](img/sRRR_poster.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
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     "slide_type": "slide"
    }
   },
   "source": [
    "![](img/sRRR_overview.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## sRRR Objective\n",
    "\n",
    "![](img/sRRR_objective.png)\n",
    "\n",
    "Reduced-Rank Regression with lasso and ridge penalty. $\\alpha$ trades off between the two ($\\alpha=0$ = pure ridge, $\\alpha=1$ = pure lasso)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Results on Patch-Seq Datasets\n",
    "\n",
    "![](img/sRRR_results.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "subslide"
    }
   },
   "source": [
    "## Error Metric\n",
    "\n",
    "![](img/sRRR_error_metric.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Interpretation of Results\n",
    "\n",
    "![](img/sRRR_interpretation.png)\n",
    "\n",
    "Plots based on PCA1/2 of $XW$ (left, selected genes) and $YV$ (right, electrophysiological properties)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "![](img/transfer_RRR_poster.png)\n",
    "![](img/transfer_RRR_overview.png)\n",
    "\n",
    "[Svanera (2019)](https://www.biorxiv.org/content/10.1101/535377v2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "slideshow": {
     "slide_type": "slide"
    }
   },
   "source": [
    "## Conlusions\n",
    "\n",
    "* Reducing the rank is a way of regularization (but not the only one)\n",
    "* On its own doesn't seem too impressive\n",
    "* Methods get generally better with more paramters and validation (not so surprising...)\n",
    "\n",
    "Should you use RRR?\n",
    "* Depends on the assumptions: linear, rank-reduced relation between $X$ and $Y$"
   ]
  }
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